Approximation spectral d'un opérateur borné et normal à l'aide de ses fonctions de la densité spectrale
Concerning some version of the Lax-Milgram Lemma in normed spaces
Concerning decomposition of a system of linear algebraic equations
On solving linear algebraic equations with an ill-conditioned matrix
Mixed nonlinear functional equations and approximation of their solutions. The theory of J. Descloux and J. Rappaz. II. Interior approximation of a branch
In part II the author investigates the inner approximate representation of solutions of the equation F(x)=0 in the neighbourhood of regular and critical points.
Review: B. N. Parlett; The symmetric eigenvalue problem
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Mixed nonlinear functional equations and approximation of their solutions. The theory of J. Descloux and J. Rappaz. I. Regular and critical points. Bifurcation
The contents of part I lie in the compilation of papers by Descloux and Rappaz ["On numerical approximation of solution branches of nonlinear equations'', École Polytech. Lausanne, Lausanne, 1981; per bibl.; RAIRO Anal. Numér. 16 (1982), no. 4, 319–349; MR0684829]. In Banach spaces the author investigates the implicit nonlinear operator equation F(x)=0 with a sufficiently smooth operator F. He formulates the notions of regular and critical points of an operator and studies the behaviour of the solutions...
The optimal explicit unconditionally stable box scheme
The finite difference “box” scheme, (see also [1],[2]), is considered on the simplest possible model of single first order linear hyperbolic equation: ut+mux=0 with constant, coefficient m, and one space variable. The optimal version of the scheme, which is nonoscilating and unconditionally stable with respect to the initial and boundary conditions, is derived in the class of box schemes of the order at, least one. If apropriately iterated, this ścinane may be applied to general systems of quasilinear...
A general scheme for obtaining estimates for interior approximation of certain operators in Banach spaces
The author gives certain schemas of approximation to certain bounded linear operators in Banach spaces by means of families of simpler operators and of approximation to solutions of linear equations. Estimates of accuracy are given, which seem to be the main aim of the paper. The very technical character of the paper makes it impossible to give here a more detailed description of the contents.
Remarks on polynomial methods for solving systems of linear algebraic equations
For a large system of linear algebraic equations , the approximate solution is computed as the -th order Fourier development of the function , related to orthogonal polynomials in space. The domain in the complex plane is assumed to be known. This domain contains the spectrum of the matrix . Two algorithms for are discussed. Two possibilities of preconditioning by an application of the so called Richardson iteration process with a constant relaxation coefficient are proposed. The case...
Sur les systèmes infinis d'équations différentielles ordinaires dans certains espaces de Fréchet
Table des Matières§ 1. Généralités. Matrices infinies............................................ 5§ 2. Systèmes infinis d'équations différentielles. Problème de Cauchy. Existence-unicité............................................................................ 10§ 3. Approximation par les systèmes finis......................................... 20§ 4. Dépendance de la solution des conditions initiales ou d'un paramètre......... 23§ 5. Quelques remarques sur la séparation des variables..............................
On a certain algorithm of eigenvalue localization for normal operators
On Jeffreys model of heat conduction
The Jeffreys model of heat conduction is a system of two partial differential equations of mixed hyperbolic and parabolic character. The analysis of an initial-boundary value problem for this system is given. Existence and uniqueness of a weak solution of the problem under very weak regularity assumptions on the data is proved. A finite difference approximation of this problem is discussed as well. Stability and convergence of the discrete problem are proved.
To readers, authors, referees, formal and informal co-workers of Matematyka Stosowana-Applied Mathematics
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