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  • Articles  (16)
  • Other Sources
  • Mathematics and Statistics  (13)
  • Convergence  (3)
  • 1980-1984  (16)
  • Mathematics  (16)
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  • Articles  (16)
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  • 1
    Electronic Resource
    Electronic Resource
    Iterative methods for variational and complementarity problems (1982)
    Springer
    Mathematical programming 24 (1982), S. 284-313 
    Details
    ISSN: 1436-4646
    Keywords: Variational Inequality ; Complementarity ; Iterative Methods ; Convergence ; Traffic Equilibria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems. Included among such methods are the Newton and several successive overrelaxation algorithms. For the most part, the study is concerned with the family of linear approximation methods. These are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems. Convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches. The paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria. Finally, several convergence results are obtained for some nonlinear approximation methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585112
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  • 2
    Electronic Resource
    Electronic Resource
    Why use population entropy? It determines the rate of convergence (1982)
    Springer
    Journal of mathematical biology 13 (1982), S. 325-337 
    Details
    ISSN: 1432-1416
    Keywords: Population entropy ; Leslie model ; Markov chain ; Convergence ; Stable age distribution ; Ergodic theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary The population entropy introduced by Demetrius is shown to have a precise dynamical meaning as a measure of convergence rate to the stable age distribution. First the Leslie population model is transformed exactly into a Markov chain on a state space of age-classes. Next the dynamics of convergence from a nonequilibrium state to the stable state are analyzed. The results provide the first clear biological reason why entropy is a broadly useful population statistic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276067
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  • 3
    Electronic Resource
    Electronic Resource
    Primitivity and convergence to stability (1981)
    Springer
    Journal of mathematical biology 13 (1981), S. 241-246 
    Details
    ISSN: 1432-1416
    Keywords: Leslie matrix ; Index of primitivity ; Convergence ; Stable age distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An exact expression for the index of primitivity g of a Leslie matrix is obtained, which applies also to time-varying matrices which share an incidence matrix. Elapsed time (not time intervals) to primitivity is shown to depend only weakly on the discretization scheme used. A lower bound for speed of convergence to the stable (fixed or time-dependent as appropriate) state is given which depends sensitively on g.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275217
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  • 4
    Electronic Resource
    Electronic Resource
    The effect of a thin inclusion of high rigidity in an elastic body (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 251-270 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study an elastic body comprising an inclusion whose thickness is 2∊ and for which Lamé's constants are λ∊ and μ. We are interested in the limit behaviour of the inclusion, when ∊ → 0 and μ∊ → ∊; that is when the inclusion becomes thiner and more rigid. Different behaviours are possible, according to the rate at which μ∊ converges to infinity; the limit inclusion may “vanish” if it is not very rigid, but also it may be entirely solid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020302
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  • 5
    Electronic Resource
    Electronic Resource
    Galerkin approximations for the equation Lu + Nu = f (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 286-290 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Introducing the concept of a supercontinuous operator, we obtain a general convergence theorem for Galerkin approximations. Under the stronger assumption that N is a monotone operator with N(0) = 0, we show norm convergence of the unique Galerkin approximations to the unique solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040119
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  • 6
    Electronic Resource
    Electronic Resource
    Mathematische Behandlung ernes Modells der Haemodialyse (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 393-404 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper a simple mathematical model for the process of hemodialysis is presented. This model is based on a system of two linear differential equations of first order with partly discontinuous coefficients that describe the time-development of the concentrations of a certain toxin (like urea) in the intra- and extracellular part of the human body. The main result is the existence of periodic positive solutions of this system under the natural assumption that the generation of the toxin and its removal by hemodialysis are periodic processes. These periodic positive solutions are also computed numerically for a realistic choice of the coefficients of the modelling differential equations.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030127
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  • 7
    Electronic Resource
    Electronic Resource
    The impedance boundary value problem for the time harmonic Maxwell equations (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 475-487 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of a unique solution to Maxwell's equations defined in an exterior domain with impedance boundary condition is established for all frequencies. This is accomplished by reducing this problem to that of solving a system of singular integral equations and then regularizing this system such that the Riesz theory is applicable. We also consider the inverse problem in which it is desired to determine the impedance from a knowledge of the far field pattern. By restricting the impedance to lie a priori in a compact set results are obtained on the existence, uniqueness, and stability of the solution to this inverse scattering problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030133
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  • 8
    Electronic Resource
    Electronic Resource
    Bifurcation problems for discrete variational inequalities (1982)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 4 (1982), S. 243-258 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The buckling of a beam or a plate which is subject to obstacles is typical for the variational inequalities that are considered here. Birfurcation is known to occur from the first eigenvalue of the linearized problem. For a discretization the bifurcation point and the bifurcating branches may be obtained by solving a constrained optimization problem. An algorithm is proposed and its convergence is proved. The buckling of a clamped beam subject to point obstacles is considered in the continuous case and some numerical results for this problem are presented.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670040116
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  • 9
    Electronic Resource
    Electronic Resource
    Faedo-galerkin approximations in equations of evolution (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 41-54 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the evolution equation u' = Au + Nu u(0) = φu is a function on a real interval [0, T] with values in a Hilbert space H, A is a linear operator in H generating a continuous semigroup eAt and N is a nonlinear operator in H.We show that 1Existence of the exact solution implies existence of the Faedo-Galerkin Approximations.2Existence of the Faedo-Galerkin Approximations implies existence of the exact solution.3Uniform convergence of the Faedo-Galerkin Approximations to the exact solution.The Paper consists of two parts. In the first five sections we require that A possesses a complete orthonormal system of eigenfunctions, in section 6 we drop this requirement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060104
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  • 10
    Electronic Resource
    Electronic Resource
    Transmutation via the momentum plane (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 467-495 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Transmutation methods are developed for equations of the form x2 ϕ“ + x2(k2” - q̃(x)) ϕ = (v2 - (1/4)) ϕ, with v as spectral variable, which correspond to problems in quantum scattering theory at fixed energy k2 (here v ˜ l + (1/2) with l complex angular momentum). Spectral formulas for transmutation kernels are constructed and the machinery of transmutation theory developed by the author for spectral variable k is shown to have a version here. General Kontrorovič-Lebedev theorems are also proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670060129
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