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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 42 (1983), S. 147-154 
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We give sufficient conditions for convergence of the chord method for a class of singular problems. The rate of convergence is sublinear.
    Materialart: Digitale Medien
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 39 (1982), S. 175-193 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS) (1980) ; Primary 65J05, 65J15 ; Secondary 47H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary For solving a nonlinear operator equationF(x)=0 in Banach spaces, the Newton's method or Newton type methods are important numerical techniques. We use the properties of real equationt=Φ(t) majorizing an operator equationx=Gx to find a fixed point ofG as a solution of equationF(x)=0. Various type of operatorsG are considered in this paper. For a nonlinear operatorG, we would find a real function Φ majorizing the operatorG and it will be related to a rate of convergence $$\omega (r) = \frac{{r^2 }}{{2(r^2 + d)^{1/2} }}.$$ It follows thatG has a fixed point as a solution ofF(x)=0. Practical limitations of error bounds like as in Potra and Pták [5] are discribed.
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  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 39 (1982), S. 325-340 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Beschreibung / Inhaltsverzeichnis: Summary In this paper we present convergence results for the asynchronous algorithms based essentially on the notion of classical contraction. We generalize, in particular, all convergence results for those algorithms which are based on the vectorial norm hypothesis, in wide spread use recently. Certain problems, for which the vectorial norm hypothesis can be difficult or even impossible to verify, can nontheless be tackled within the scope of the classical contraction that we adopte.
    Notizen: Resumé Nous présentons dans cet article des résultats de convergence des algorithmes asynchrones basés essentiellement sur la notion classique de contraction. Nous généralisons, en particulier, tous les résultats de convergence de ces algorithmes qui font l'hypothèse de contraction en norme vectorielle qui récemment a été très souvant utilisée. Par ailleurs, l'hypothèse de contraction en norme vectorielle peut se trouver difficile, voire impossible à vérifier pour certains problèmes qui peuvent être cependant abordés dans le cadre de la contraction classique que nous adoptons.
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 39 (1982), S. 429-448 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65K05 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper considers local convergence properties of inexact partitioned quasi-Newton algorithms for the solution of certain non-linear equations and, in particular, the optimization of partially separable objective functions. Using the bounded deterioration principle, one obtains local and linear convergence, which impliesQ-superlinear convergence under the usual conditions on the quasi-Newton updates. For the optimization case, these conditions are shown to be satisfied by any sequence of updates within the convex Broyden class, even if some Hessians are singular at the minimizer. Finally, local andQ-superlinear convergence is established for an inexact partitioned variable metric method under mild assumptions on the initial Hessian approximations.
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  • 5
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 40 (1982), S. 111-117 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We seek an approximation to a zero of a continuous functionf:[a,b]→ℝ such thatf(a)≦0 andf(b)≧0. It is known that the bisection algorithm makes optimal use ofn function evaluations, i.e., yields the minimal error which is (b−a)/2 n+1, see e.g. Kung [2]. Traub and Wozniakowski [5] proposed using more general information onf by permitting the adaptive evaluations ofn arbitrary linear functionals. They conjectured [5, p. 170] that the bisection algorithm remains optimal even if these general evaluations are permitted. This paper affirmatively proves this conjecture. In fact we prove optimality of the bisection algorithm even assuming thatf is infinitely many times differentiable on [a, b] and has exactly one simple zero.
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  • 6
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 42 (1983), S. 323-329 
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65K05 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A Newton-like iteration scheme is proposed for the tracing of an implicitly defined smooth curve. This scheme originates from the study of the continuous Newton-Raphson method for underdetermined systems and, hence, inherits the characteristic property of orthogonality. Its domain of attraction is formed and makes it possible to trace this curve more efficiently.
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  • 7
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 24 (1981), S. 71-84 
    ISSN: 1432-0630
    Schlagwort(e): 32 ; 42.65
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract We consider cooling of a trapped particle in the limit when the position and velocity variables do not change adiabatically. The slowly varying quantity in a harmonic trap is then the energy, and a representation based on oscillator eigenstates is used. For large excitation, fast particles, a Fokker-Planck expansion is obtained which is valid when our adiabatic description breaks down. Estimates of the initial cooling rate are given and compared with earlier results. Our treatment requires a large number of oscillator states to be coupled by each one-photon process, and in this limit the diffusion will make the expansion invalid towards the end of the cooling; our physical interpretation is that particles leak out of the trap. The opposite case, the Lamb-Dicke regime, is advantageous for cooling experiments, and then a difference equation replaces the Fokker-Planck equation of the present paper.
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  • 8
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 31 (1983), S. 195-199 
    ISSN: 1432-0630
    Schlagwort(e): 42.65 ; 71.20
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract We report on measurements of spin-flip Raman gain inn-Hg1−x Cd x Te (x=0.23, carrier density 1.0×1015cm−3) as a function of the magnetic field up to 1.6T. The measurements were carried out by a small signal gain technique at a temperature of 1.8 K. Furthermore, the measurements yield lineshapes and linewidths of the spontaneous scattering and allow a precise determination of the effectiveg-value. The highest gain observed is 0.2 cm/W. The band edge value of the effectiveg-value is −93.2 and the widths of the symmetric lines are between 18 and 120 G, depending on the magnetic field.
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  • 9
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 24 (1981), S. 119-120 
    ISSN: 1432-0630
    Schlagwort(e): 42.65
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract A technique of fast deep cooling of atomic or molecular buffer gases by laser radiation is proposed. With Na vapor as a cooling agent interacting with a laser field a cooling time of about 10−3s and minimum temperature of about 25K can be attained.
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  • 10
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 24 (1981), S. 89-106 
    ISSN: 1432-0630
    Schlagwort(e): 33 ; 42.65 ; 82.50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract A review of laser-induced photoionization of polyatomic molecules and the application of this process in mass-spectrometry is presented. Combination of laser selective photoionization and mass spectral analysis of fragments as a promising tool for the detection of trace amounts of complex molecules is considered particularly.
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  • 11
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 24 (1981), S. 349-355 
    ISSN: 1432-0630
    Schlagwort(e): 42.65
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract We construct field equations and generalised Bloch equations for multiphoton processes involving the coherent interaction of a number of distinct electric fields with an arbitrary number of atomic eigenstates, and apply the equations to some physical examples. Transient stimulated hyper-Raman scattering, in the low-conversion regime and far from saturation, has been studied analytically. Assuming that the pump pulse interacts with the medium byn-photon absorption, we find expression for the intensity of the generated Stokes pulse.
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  • 12
    ISSN: 1432-0630
    Schlagwort(e): 42.60 ; 42.65
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract In this paper we describe the construction of a monochromatic and frequency stabilized continuous wave (cw) source in the 5 μm region. It is built up by a cw single line, single-mode frequency and amplitude stabilized CO2 laser. This primary CO2 laser source is then frequency-doubled in a tellurium crystal using second harmonic generation (SHG). The obtained emission is monochromatic (half-width 50 kHz). The frequency can be varied discreetly from 4.6 μm to 5.5 μ depending on the CO2 laser line chosen.
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  • 13
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 24 (1981), S. 11-12 
    ISSN: 1432-0630
    Schlagwort(e): 42.65 ; 07.65 ; 33.90
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract Experimental observation of optical Ramsey interference in saturated absorption of methane in a low-pressure gas cell with three spacially separated laser beams at 3.39 μm is reported.
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  • 14
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 25 (1981), S. 31-34 
    ISSN: 1432-0630
    Schlagwort(e): 35 ; 42.55 ; 42.65
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract The decay rates of the3 D 1 level of I–II and the 3s 2 level of neon have been measured by the magnetic-field power dip method. The decay rate at the zero-pressure limit is found to be 7.1 MHz/2π for the3 D 1 level. The collision cross-section for excited I ions with helium atoms equals 0.19×10−15 cm2.
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  • 15
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 25 (1981), S. 49-56 
    ISSN: 1432-0630
    Schlagwort(e): 42.65 ; 78.20
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract Four-wave mixing with two circularly polarized counter-propagating waves inducing a helical birefringence structure can be used to measure a number of material parameters of a liquid crystalline medium. Application to a cholesteric substance is particularly interesting. A resonant effect is expected when the induced helix has a pitch coinciding with the natural helical pitch of the medium towards the isotropic → cholesteric transition. Field-induced shift in the transition temperature is also expected.
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  • 16
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 26 (1981), S. 185-190 
    ISSN: 1432-0630
    Schlagwort(e): 42.65
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract Optical frequency mixing through nonlinear mode coupling in a planar waveguide, fabricated with a cubic or uniaxial dielectric, is discussed. A threewave interaction is examined and the optimum crystal orientations that lead to the highest efficiency are determined in those particular cases in which they do not depend on the field distribution of the modes. The analysis is carried out in detail for cubic crystals; sensitivity to misalignments is also studied and numerical results are reported.
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  • 17
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 32 (1983), S. 135-140 
    ISSN: 1432-0630
    Schlagwort(e): 42.65 ; 64.60 ; 78.90 ; 81.40
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract We report the observation and analysis of higher-order optical diffraction patterns arising from linear combinations of the primary laser-induced gratings or ripples on germanium surfaces. These higher-order surface structures presumably arise from nonlinear interactions between superimposed primary gratings with different grating wave vectors. For gratings produced by normally incident laser beams on Ge 〈111〉 surfaces, the diffraction patterns exhibit a strongly hexagonal symmetry.
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  • 18
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 24 (1981), S. 45-48 
    ISSN: 1432-0630
    Schlagwort(e): 42.55 ; 42.65 ; 64
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract We investigated time-dependent effects related to the bistable operation of a CO2 laser with an intracavity nonlinear absorber (SF6). The response of the system to small perturbations was sensitively dependent on the operating laser line [P(12)→P(30)] of the 10.6 μm band. The narrow bistable region forP(12), due to a very narrow hysteresis loop, can be effectively utilized for optical switching, because of its pronounced sensitivity to variations in operational parameters. The maximum admissable beam blocking time (intracavity) for spontaneous return to lasing was measured forP(16), for a range of absorber pressures. This τm is related to the relaxation time of the upper level in the absorber.
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  • 19
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 24 (1981), S. 139-142 
    ISSN: 1432-0630
    Schlagwort(e): 42.65
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract The tuning and threshold behaviors of 5P 1/2–5P 3/2 stimulated electronic Raman scattering in In vapor were investigated. The Stokes output intensity was limited by atom depletion process in the atomic density available for the measurement. The anti-Stokes radiation observed was studied in terms of the phase matching condition.
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  • 20
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 24 (1981), S. 151-162 
    ISSN: 1432-0630
    Schlagwort(e): 32 ; 42.65
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract In this paper we consider the laser cooling of a trapped particle when the discrete nature of the quantum levels must be taken into account. We particularize the equations to the Lamb-Dicke limit when the oscillational, amplitude is much less than the optical wavelength. Then the quantum levels are coupled only to the neighbouring ones, and we can also find a small parameter to use for adiabatic elimination of rapidly varying terms. There emerges one rate equation for the probability distribution over the quantum states. The ultimate distribution is found to be of the Planckian type independently of the initial one. We solve the equation, generally and obtain the time evolution for an arbitrary initial distribution. In particular we look at an initially thermal, Poisson, or pure state distribution. For the thermal one we find that its shape is preserved during the cooling. The results are discussed.
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  • 21
    ISSN: 1432-0630
    Schlagwort(e): 42.65 ; 71.20
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract We studied the change in Spin-flip Raman (SFR) gain and behaviour of the effectiveg-value as a function of pulsed electric fields inn-type InSb. The samples were held at 1.8 K in magnetic fields up to 1.4 T. Varying the strength of a pulsed electric field applied to the samples parallel to the magnetic field we found a direct correlation between the increase in electron temperature and the decrease of the Raman gain. Measurements of the Raman gain and spontaneous line width at different times after the starting of the electric pulse and during its fall time with a time resolution of 10 ns give no indication of a motional narrowing of the SFR line and of an increase of the gain during the decrease of the electric field pulse. These two predictions were made by Mooradian et al. (1972) to explain the observed transient increase of the intensity of the stimulated SFR Stokes radiation after an electric field across the sample was switched off. With our direct measurement of the Raman gain we could establish that at any time during and after the electric field pulse, the gain is less or equal to the value without electric field. In the electric field region from 0.3 V/cm up to 0.6 V/cm the Raman gain shows several maxima, originating from SFR scattering between different spin splitted conduction band levels. The electron distribution under pulsed electric field conditions give rise to a dynamically varying absorption mechanism of transmitted radiation. Time resolved transmission measurements explain the observed increase of stimulated SFR Stokes radiation during the switch-off time of electric field pulses by a lower absorption of radiation and not by a larger gain.
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  • 22
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 24 (1981), S. 303-306 
    ISSN: 1432-0630
    Schlagwort(e): 42.65
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract This paper describes the experimental investigation of stimulated Raman scattering obtained from a multimode fiber. 10 orders of stimulated Stokes scattering of wavelengths in the 546–702 nm region were obtained from a 480m multimode, low-loss, graded-index quartz fiber pumped by a 532 nm frequency-doubled YAG-Nd laser beam with a pulse duration of 7 ns, output power of 0.7 MW and repetition rates of 5 and 10 pps.
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  • 23
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 40 (1982), S. 93-98 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65D15 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Der Quotienten-Differenzen-Algorithmus nach Rutishauser ist geeignet zur Bestimmung von Polen meromorpher Funktionen, gegeben durch eine Taylorreihe. Sind mehrere Pole betragsgleich, so kann eine Polynomfolge bestimmt werden, deren Grenzpolynom diese Pole als Nullstellen hat. Die Konvergenz wurde von Rutishauser jedoch nicht bewiesen. Ein Beweis wird in der vorliegenden Arbeit präsentiert.
    Notizen: Summary The Quotient-Difference Algorithm of Rutishauser can be used for the determination of poles of a meromorphic function given by its power series. If some of the poles have same modulus, a sequence of polynomials can be determined such that the limiting polynomial has exactly these poles as zeros. The convergence has not been proved by Rutishauser, however. A proof is presented in this paper.
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  • 24
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 42 (1983), S. 31-50 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65J10 ; 41A25 ; 41A65 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Error bounds are given for the iterative computation of the eigenvectors in the Rayleigh-Schrödinger series. These bounds remove the discrepancy in the theoretical behaviour and numerical results, noted by Redont, under the assumption of collectively compact convergence. As a particular case, it follows that the eigenvector in the iterative Galerkin method proposed by Sloan improves upon the eigenvector in the Galerkin method. This is illustrated by numerical experiments.
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  • 25
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 42 (1983), S. 97-105 
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65K05 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Generalized conjugate gradient algorithms which are invariant to a nonlinear scaling of a strictly convex quadratic function are described. The algorithms when applied to scaled quadratic functionsf∶R n →R 1 of the formf(x)=h(F(x)) withF(x) strictly convex quadratic andh∈C 1(R 1) an arbitrary strictly monotone functionh generate the same direction vectors as for the functionF without perfect steps.
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  • 26
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 37 (1981), S. 93-104 
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65H05 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A recursive method is presented for computing a simple zero of an analytic functionf from information contained in a table of divided differences of its reciprocalh=1/f. A good deal of flexibility is permitted in the choice of ordinate and derivative values, and in the choice of the number of previous points upon which to base the next estimate of the required zero. The method is shown to be equivalent to a process of fitting rational functions with linear numerators to data sampled fromf. Asymptotic and regional convergence properties of such a process have already been studied; in particular, asymptotically quadratic convergence is easily obtained, at the expense of only one function evaluation and a moderate amount of “overhead” computation per step. In these respects the method is comparable with the Newton form of iterated polynomial inverse interpolation, while its regional convergence characteristics may be superior in certain circum-stances. It is also shown that the method is not unduly sensitive to round-off errors.
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  • 27
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1981), S. 209-218 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65K05 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In this paper the problem of minimizing the functionalf:D∈R n →R is considered. Typical assumptions onf are assumed. A class of Quasi-Newton methods, namely Huang's class of methods is used for finding an optimal solution of this problem. A new theorem connected with this class is presented. By means of this theorem some convergence results known up till now only for the methods which satisfy Quasi-Newton condition are extended, that is the results of superlinear convergence of variable metric methods in the cases of exact and asymptotically exact minimization and the so-called direct-prediction case. This theorem allows to interpretate one of the parameters as the scaling parameter.
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  • 28
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1981), S. 219-228 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65K05 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In this paper new Quasi-Newton methods of rank-one type for solving the unconstrained minimization problem are developed. The methods belong to the Oren-Luenberger class (for negative parametersΘ k ) and they generate always positive definite updating matrices. Moreover it is shown that these methods are invariant by scaling of the objective function.
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  • 29
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1981), S. 229-244 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65 K05 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary It is shown that the methods developed in part I of this paper [6] converge at leastn-step quadratically to the global minimum point of the objective functionf, if the Hessian off is uniformly positive definite, uniformly bounded and Lipschitz continuous and if the method is used with restart and asymptotically exact line search.
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  • 30
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1982), S. 383-392 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Recently an iterative method for the solution of systems of nonlinear equations having at leastR-order 1+ $$\sqrt 2 $$ for simple roots has been investigated by the author [7]; this method uses as many function evaluations per step as the classical Newton method. In the present note we deal with several properties of the method such as monotone convergence, asymptotic inclusion of the solution and convergence in the case of multiple roots.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 31
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1982), S. 393-416 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 49D05, 49D07, 65K10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A method for approximating the optimal control and the optimal state for a class of distributed control problems governed by variational inequalities is given. It uses a Rayleigh-Ritz-Galerkin scheme, regularising techniques and a gradient algorithm. A numerical example is given.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 32
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1982), S. 427-445 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS) 65J15, 65G99 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Sharp a priori and a posteriori error bounds are given for the secant method for solving non-linear equations in Banach spaces. The numerical stability of this method is also investigated. The stability results are analogous to those obtained by Lancaster for Newton's method.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 33
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1982), S. 455-465 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10, 47H17 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A numerical technique is described for computing turning points of a space curveL implicitly defined by a nonlinear system ofn equations inn+1 variables. The basic idea is a local parametrization ofL where the parameter that gives the next iterate is determined by applying one step of the well-known method for minimizing a real function using cubic Hermite interpolation with two nodes. The method is shown to convergeQ-super-linearly and withR-order of at least two. A numerical example concerning the analysis of nonlinear resistive circuits shows the algorithm to work effectively on real life problems.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 34
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 37 (1981), S. 433-444 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary An iterative method is presented for determining a turning point in a branch of solutions of an algebraic system of equations depending on a parameter. One shows that the convergence is superlinear and that this method may constitute a complement for the Newton method. With a finite element method, numerical results are given testing the process on the discrete version of a mildly nonlinear boundary value problem to determine the turning point in the positive solution branch.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 35
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 37 (1981), S. 279-295 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H 10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We derive a class of globally and quadratically converging algorithms for a system of nonlinear equations,g(u)=0, whereg is a sufficiently smooth homeomorphism. Particular attention is directed to key parameters which control the iteration. Several examples are given that have been successful in solving the coupled nonlinear PDEs which arise in semiconductor device modelling.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 36
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 37 (1981), S. 445-452 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A finite element method (P1) with numerical integration for approximating the boundary value problem −Δu=λe u is considered. It is shown that the discrete problem has a solution branch (with turning point) which converges uniformely to a solution branch of the continuous problem. Error estimates are given; for example it is found that $$\left| {\lambda _0 - \lambda _h^0 } \right| = 0(h^{2 - \varepsilon } )$$ , ɛ〉0, whereλ 0 andλ h 0 are critical values of the parameter λ for continuous and discrete problems.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 37
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 39 (1982), S. 119-137 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper presents a minimization method based on the idea of partitioned updating of the Hessian matrix in the case where the objective function can be decomposed in a sum of convex “element” functions. This situation occurs in a large class of practical problems including nonlinear finite elements calculations. Some theoretical and algorithmic properties of the update are discussed and encouraging numerical results are presented.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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