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Details for:
Dyakonov E. Optimization in Solving Elliptic Problems 2018
dyakonov e optimization solving elliptic problems 2018
Type:
E-books
Files:
1
Size:
14.6 MB
Uploaded On:
Oct. 4, 2022, 10:35 a.m.
Added By:
andryold1
Seeders:
2
Leechers:
0
Info Hash:
B982B3B9F1480CE2E14A13336838B03F1F12E205
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Textbook in PDF format Preface Editor's Preface The Author The Editor Basic Notation Introduction Modern formulations of elliptic boundary value problems Variational principles of mathematical physics Variational problems in a Hilbert space Completion of a preHilbert space and basic properties of Sobolev spaces Generalized solutions of elliptic boundary value problems Projective-grid methods (finite element methods) Rayleigh-Ritz method Bubnov-Galerkin method and projective methods Projective-grid methods (finite element methods)2.4. The simplest projective-grid operators Composite grids and triangulations local grid refinement Methods of solution of discretized problems asymptotically optimal and nearly optimal preconditioners Specificity of grid systems direct methods Classical iterative methods Iterative methods with spectrally equivalent operators optimal preconditioning Symmetrizations of systems Coarse grid continuation (multigrid acceleration of the basic iterative algorithm) Some nonelliptic applications Invariance of operator inequalities under projective approximations Rayleigh-Ritz method and Gram matrices Projective approximations of operators Spectral equivalence of grid operators defined on topologically equivalent triangulations Spectral equivalence of grid operators defined on composite triangulations with local refinements N-widths of compact sets and optimal numerical methods for classes of problems Approximations of compact sets and criteria for optimality of computational algorithms Iterative methods with model symmetric operators Estimates of rates of convergence in the Euclidean space H(B) of the modified method of the simple iteration Estimates of the rate of convergence in the Euclidean space H(B2) Condition numbers of symmetrized linear systems generalizations for nonlinear problems A posteriori estimates Modifications of Richardson's iteration Use of orthogonalization Adaptation of iterative parameters Modified gradient methods Nonsymmetric model operators
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Dyakonov E. Optimization in Solving Elliptic Problems 2018.pdf
14.6 MB
