ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Articles  (10)
  • 65H10  (5)
  • AMS(MOS): 65D15  (5)
  • Springer  (10)
  • American Chemical Society
  • Annual Reviews
  • Blackwell Publishing Ltd
  • Elsevier
  • Wiley
  • 2005-2009
  • 1990-1994
  • 1980-1984  (10)
  • 2008
  • 1982  (10)
  • Mathematics  (6)
  • Computer Science  (4)
Collection
  • Articles  (10)
Source
Keywords
Publisher
  • Springer  (10)
  • American Chemical Society
  • Annual Reviews
  • Blackwell Publishing Ltd
  • Elsevier
    • +
Years
  • 2005-2009
  • 1990-1994
  • 1980-1984  (10)
Year
Topic
  • Mathematics  (6)
  • Computer Science  (4)
  • 1
    Electronic Resource
    Electronic Resource
    Spurious solutions for discrete superlinear boundary value problems (1982)
    Springer
    Computing 28 (1982), S. 43-51 
    Details
    ISSN: 1436-5057
    Keywords: spurious solutions ; discretizations ; nonlinear eigenvalue problems ; superlinear functions ; 34B15 ; 65H10 ; 65L10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden endlich dimensionale, nichtlineare Eigenwertprobleme der FormAu=λFu mit einer MatrixA und einem Feld(Fu) i =f(u i ),i=1, ...,m betrachtet. Diese können als Diskretisierung eines entsprechenden Randwertproblems angesehen werden. Wir zeigen, daß diese diskreten Gleichungen dann zusätzliche, positive Lösungszweige (welche in [1,7] beobachtet wurden) aufweisen, wennf hinreichend stark wächst undA −1 mindestens zwei positive Spalten von einem bestimmten Typ besitzt. Ausführlicher, werden die Fällef(u)=e u undf(u)=u α behandelt, für die auch diskrete Verzweigungsdiagramme angegeben werden.
    Notes: Abstract We consider finite dimensional nonlinear eigenvalue problems of the typeAu=λFu whereA is a matrix and(Fu) i =f(u i ),i=1, ...,m. These may be thought of as discretizations of a corresponding boundary value problem. We show that positive, spurious solution branches of the discrete equations (which have been observed in some cases in [1, 7]) typically arise iff increases sufficiently strong and ifA −1 has at least two positive columns of a certain type. We treat in more detail the casesf(u)=e u andf(u)=u α where also discrete bifurcation diagrams are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02237994
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    On global convergence of coordinate relaxation in the case of an unsymmetrical, diagonally dominant Jacobian (1982)
    Springer
    Computing 28 (1982), S. 345-361 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 65N20 ; Coordinate relaxation ; global convergence ; diagonal dominance ; discrete obstacle problems ; quasilinear elliptic equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden einige neue Konvergenzsätze für eine allgemeine Klasse von Koordinatenrelaxationen zur Lösung nichtlinearer Gleichungssysteme bewiesen. Dabei wird die Existenz einer Skalierung der abhängigen oder unabhängigen Variablen vorausgesetzt, so daß die entstehende Funktionalmatrix spalten- bzw. zeilendiagonaldominant ist. Einer dieser Sätze wird übertragen auf die „Koordinatenrelaxation mit Projektion” zur Lösung diskretisierter Hindernisprobleme. Schließlich werden Beispiele zur Anwendbarkeit gegeben.
    Notes: Abstract We prove some new theorems on global convergence for a general class of coordinate relaxation schemes to solve systems of nonlinear equations. Those systems are assumed to admit a scaling of the dependent or independent variables such that the arising Jacobian is column or row diagonally dominant, resp. We extend one of these theorems to the case of coordinate relaxation with projection to solve discrete obstacle problems, and give examples for the application.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02279817
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Solving nonlinear systems with least significant bit accuracy (1982)
    Springer
    Computing 29 (1982), S. 183-200 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 65G05 ; 65D99 ; Automatic verification ; existence ; uniqueness ; inclusion ; rounding error ; condition number ; residue
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Im folgenden wird ein Algorithmus zur Konstruktion einer Einschließung einer Lösung eines nichtlinearen Gleichungssystems angegeben. Im Gegensatz zu bekannten Methoden benötigt der Algorithmus keine schwierig verifizierbaren Voraussetzungen wie etwa die Nichtsingularität einer Matrix. Tatsächlich wird diese Eigenschaft vom Algorithmus automatisch verifiziert. Die Ergebnisse des Algorithmus zeichnen sich durch hohe Genauigkeit aus. Diese wird durch Residuen (eventuell höherer Ordnung) erreicht.
    Notes: Abstract We give an algorithm for constructing an inclusion of the solution of a system of nonlinear equations. In contrast to existing methods, the algorithm does not require properties which are difficult to verify such as the non-singularity of a matrix. In fact this latter property is demonstrated by the algorithm itself. The highly accurate computational results are obtained in terms of a residue of first or higher order of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02241697
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    A comparison of methods for determining turning points of nonlinear equations (1982)
    Springer
    Computing 29 (1982), S. 201-226 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 73H05 ; Turning points ; algorithms ; experimental comparison
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In vielen Gleichgewichtsproblemen ist die Bestimmung der Lage von Umkehrpunkten von Bedeutung, wo möglicherweise ein Stabilitätsverlust eintreten kann. Eine Anzahl von Algorithmen für die Berechnung solcher Punkte ist bekannt. Diese Arbeit enthält experimentelle Vergleichsresultate für insgesamt sechzehn Variationen von zehn solchen Methoden. Hierfür wurden sieben Versuchsprobleme verschiedener Dimension mit 27 Umkehrpunkten benutzt. Die Resultate deuten auf eine Reihe von Schlüssen über den relativen praktischen Wert dieser Methoden.
    Notes: Abstract In the study of many equilibrium problems it is important to determine the location of turning points which may signify a loss of stability. A number of algorithms is known for the computation of such points. In this paper experimental comparisons are presented of a total of sixteen variations of ten such methods. For this a set of seven test problems of varying dimension with a total of 27 turning points were used. The results suggest a number of conclusions about the relative practical merits of these methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02241698
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Solution of finite systems of equations by interval iteration (1982)
    Springer
    BIT 22 (1982), S. 233-251 
    Details
    ISSN: 1572-9125
    Keywords: 65G10 ; 65H05 ; 65H10 ; 65H15 ; 65F10 ; 65F15 ; Interval analysis ; interval iteration ; linear and nonlinear systems of equations ; upper and lower bounds for solutions ; eigenvalues ; and eigenvectors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In actual practice, iteration methods applied to the solution of finite systems of equations yield inconclusive results as to the existence or nonexistence of solutions and the accuracy of any approximate solutions obtained. On the other hand, construction of interval extensions of ordinary iteration operators permits one to carry out interval iteration computationally, with results which can give rigorous guarantees of existence or nonexistence of solutions, and error bounds for approximate solutions. Examples are given of the solution of a nonlinear system of equations and the calculation of eigenvalues and eigenvectors of a matrix by interval iteration. Several ways to obtain lower and upper bounds for eigenvalues are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01944479
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    The ɛ-algorithm and multivariate Padé-approximants (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 39-46 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In the univariate case the ɛ-algorithm of Wynn is closely related to the Padé-table in the following sense: if we apply the ɛ-algorithm to the partial sums of the power series $$f(x) = \sum\limits_{i = 0}^\infty {c_i x^i } $$ then ε 2m l−m is the (l, m) Padé-approximant tof(x) wherel is the degree of the numerator andm is the degree of the denominator [1 pp. 66–68]. Several generalizations of the ɛ-algorithm exist but without any connection with a theory of Padé-approximants. Also several definitions of the Padé-approximant to a multivariate function exist, but up till now without any connection with the ɛ-algorithm. In this paper, we see that the multivariate Padé-approximants introduced in [3], satisfy the same property as the univariate Padé-approximants: if we apply the ɛ-algorithm to the partial sums of the power series $$f\left( {x_1 ,...,x_n } \right) = \sum\limits_{i_1 + ... + i_n = 0}^\infty {c_{i_1 ...i_n } x_1^{i_1 } ...x_n^{i_n } } $$ then ε 2m (l−m) is the (l, m) multivariate Padé-approximant tof(x 1, ...,x n ).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01459073
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Solving complex approximation problems by semiinfinite - finite optimization techniques: A study on convergence (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 411-420 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We transform a complex approximation problem into an equivalent semiinfinite optimization problem whose constraints are described in terms of a quantity ϕ∈[0,2π[=I. We study the effect of disturbing the problem by replacingI by a compact subsetM⊂I which includes as special case the discrete case whereM consists only of finitely many points. We introduce a measure ɛ for the deviation ofM fromI and show that in any complex approximation problem the minimal distance of the disturbed problem converges quadratically with ɛ→0 to the minimal distance of the undisturbed problem which is a generalization of a result by Streit and Nuttall. We also show that in a linear finite dimensional approximation problem the convergence of the coefficients of the disturbed problem is in general at most linear. There are some graphical representations of best complex approximations computed with the described method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01407872
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Quotienten-Differenzen-Algorithmus: Beweis der Regeln von Rutishauser (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 93-98 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: 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.
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01459078
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    Unicity of best one-sidedL 1-approximations (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 229-243 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper deals with the problem of uniqueness in one-sidedL 1-approximation. The chief purpose is to characterize finite dimensional subspacesG of the space of continuous or differentiable functions which have a unique best one-sidedL 1-approximation. In addition, we study a related problem in moment theory. These considerations have an important application to the uniqueness of quadrature formulae of highest possible degree of precision.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400541
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Optimal cycles in doubly weighted graphs and approximation of bivariate functions by univariate ones (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 65-84 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65D15 ; CR: 5.13
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The problem of finding optimal cycles in a doubly weighted directed graph (Problem A) is closely related to the problem of approximating bivariate functions by the sum of two univariate functions with respect to the supremum norm (Problem B). The close relationship between Problem A and Problem B is detected by the characterization (7.4) of the distance dist (f, t) of Problem B. In Part 1 we construct an algorithm for Problem A where the essential role is played by the minimal lengthsy j(k) defined by (2.3). If weight functiont≡1 then the minimum of Problem A is computed by equality (2.4). Ift≡1 then the minimum is obtained by a binary search procedure, Algorithm 3. In Part 2 we construct our algorithms for solving Problem B by following exactly the ideas of Part 1. By Algorithm 4 we compute the minimal pseudolengthsh k(y, M) defined by (7.5). If weight functiont≡1 then the infimum dist(f,t) of Problem B is obtained by equality (7.12) which is closely related to (2.4). Ift≢1 we compute the infimum dist(f,t) by the binary search procedure Algorithm 5. Additionally, Algorithm 4 leads to a constructive proof of the existence of continuous optimal solutions of Problem B (see Theorem 7.1e) which is already known in caset≡1 but unknown in caset≢1. Interesting applications to the steady-state behaviour of industrial processes with interference (Sect. 3) and the solution of integral equations (Problem C) are included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399312
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...