Numerical Methods Grid Equations (53 results)

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Softcover. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 65 SAM Vol.1 9783764322762 Sprache: Englisch Gewicht in Gramm: 550.

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Druck auf Anfrage Neuware - Printed after ordering - 5 The Mathematical Theory of Iterative Methods.- 5.1 Several results from functional analysis.- 5.1.1 Linear spaces.- 5.1.2 Operators in linear normed spaces.- 5.1.3 Operators in a Hilbert space.- 5.1.4 Functions of a bounded operator.- 5.1.5 Operators in a finite-dimensional space.- 5.1.6 The solubility of operator equations.- 5.2 Difference schemes as operator equations.- 5.2.1 Examples of grid-function spaces.- 5.2.2 Several difference identities.- 5.2.3 Bounds for the simplest difference operators.- 5.2.4 Lower bounds for certain difference operators.- 5.2.5 Upper bounds for difference operators.- 5.2.6 Difference schemes as operator equations in abstract spaces.- 5.2.7 Difference schemes for elliptic equations with constant coefficients.- 5.2.8 Equations with variable coefficients and with mixed derivatives.- 5.3 Basic concepts from the theory of iterative methods.- 5.3.1 The steady state method.- 5.3.2 Iterative schemes.- 5.3.3 Convergence and iteration counts.- 5.3.4 Classification of iterative methods.- 6 Two-Level Iterative Methods.- 6.1 Choosing the iterative parameters.- 6.1.1 The initial family of iterative schemes.- 6.1.2 The problem for the error.- 6.1.3 The self-adjoint case.- 6.2 The Chebyshev two-level method.- 6.2.1 Construction of the set of iterative parameters.- 6.2.2 On the optimality of the a priori estimate.- 6.2.3 Sample choices for the operator D.- 6.2.4 On the computational stability of the method.- 6.2.5 Construction of the optimal sequence of iterative parameters.- 6.3 The simple iteration method.- 6.3.1 The choice of the iterative parameter.- 6.3.2 An estimate for the norm of the transformation operator.- 6.4 The non-self-adjoint case. The simple iteration method.- 6.4.1 Statement of the problem.- 6.4.2 Minimizing the norm of the transformation operator.- 6.4.3 Minimizing the norm of the resolving operator.- 6.4.4 The symmetrization method.- 6.5 Sample applications of the iterative methods.- 6.5.1 A Dirichlet difference problem for Poisson¿s equation in a rectangle.- 6.5.2 A Dirichlet difference problem for Poisson¿s equation in an arbitrary region.- 6.5.3 A Dirichlet difference problem for an elliptic equation with variable coefficients.- 6.5.4 A Dirichlet difference problem for an elliptic equation with mixed derivatives.- 7 Three-Level Iterative Methods.- 7.1 An estimate of the convergence rate.- 7.1.1 The basic family of iterative schemes.- 7.1.2 An estimate for the norm of the error.- 7.2 The Chebyshev semi-iterative method.- 7.2.1 Formulas for the iterative parameters.- 7.2.2 Sample choices for the operator D.- 7.2.3 The algorithm of the method.- 7.3 The stationary three-level method.- 7.3.1 The choice of the iterative parameters.- 7.3.2 An estimate for the rate of convergence.- 7.4 The stability of two-level and three-level methods relative to a priori data.- 7.4.1 Statement of the problem.- 7.4.2 Estimates for the convergence rates of the methods.- 8 Iterative Methods of Variational Type.- 8.1 Two-level gradient methods.- 8.1.1 The choice of the iterative parameters.- 8.1.2 A formula for the iterative parameters.- 8.1.3 An estimate of the convergence rate.- 8.1.4 Optimality of the estimate in the self-adjoint case.- 8.1.5 An asymptotic property of the gradient methods in the self-adjoint case.- 8.2 Examples of two-level gradient methods.- 8.2.1 The steepest-descent method.- 8.2.2 The minimal residual method.- 8.2.3 The minimal correction method.- 8.2.4 The minimal error method.- 8.2.5 A sample application of two-level methods.- 8.3 Three-level conjugate-direction methods.- 8.3.1 The choice of the iterative parameters. An estimate of the convergence rate.- 8.3.2 Formulas for the iterative parameters. The three-level iterative scheme.- 8.3.3 Variants of the computational formulas.- 8.4 Examples of the three-level methods.- 8.4.1 Special cases of the conjugate-direction methods.- 8.4.2 Locally optimal three-level methods.- 8.5 Accelerating the convergence of two-level methods in the self-adjoint case.- 8.5.1 An algorithm for the acceleration process.- 8.5.2 An estimate of the effectiveness.- 8.5.3 An example.- 9 Triangular Iterative Methods.- 9.1 The Gauss-Seidel method.- 9.1.1 The iterative scheme for the method.- 9.1.2 Sample applications of the method.- 9.1.3 Sufficient conditions for convergence.- 9.2 The successive over-relaxation method.- 9.2.1 The iterative scheme. Sufficient conditions for covergence.- 9.2.2 The choice of the iterative parameter.- 9.2.3 An estimate of the spectral radius.- 9.2.4 A Dirichlet difference problem for Poisson¿s equation in a rectangle.- 9.2.5 A Dirichlet difference problem for an elliptic equation with variable coefficients.- 9.3 Triangular methods.- 9.3.1 The iterative scheme.- 9.3.2 An estimate of the convergence rate.- 9.3.3 The choice of the iterative parameter.- 9.3.4 An estimate for the convergence rates of the Gauss-Seidel and relaxation methods.- 10 The Alternate-Triangular Method.- 10.1 The general theory of the method.- 10.1.1 The iterative scheme.- 10.1.2 Choice of the iterative parameters.- 10.1.3 A method for finding and .- 10.1.4 A Dirichlet difference problem for Poisson¿s equation in a rectangle.- 10.2 Boundary-value difference problems for elliptic equations in a rectangle.- 10.2.1 A Dirichlet problem for an equation with variable coefficients.- 10.2.2 A modified alternate-triangular method.- 10.2.3 A comparison of the variants of the method.- 10.2.4 A boundary-value problem of the third kind.- 10.2.5 A Dirichlet difference problem for an equation with mixed derivatives.- 10.3 The alternate-triangular method for elliptic equations in arbitrary regions.- 10.3.1 The statement of the difference problem.- 10.3.2 The construction of an alternate-triangular method.- 10.3.3 A Dirichlet problem for Poisson¿s equation in an arbitrary region.- 11 The Alternating-Directions Method.- 11.1 The alternating-directions method in the commutative case.- 11.1.1 The i.

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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - The finite-difference solution of mathematical-physics differential equations is carried out in two stages: 1) the writing of the difference scheme (a differ ence approximation to the differential equation on a grid), 2) the computer solution of the difference equations, which are written in the form of a high order system of linear algebraic equations of special form (ill-conditioned, band-structured). Application of general linear algebra methods is not always appropriate for such systems because of the need to store a large volume of information, as well as because of the large amount of work required by these methods. For the solution of difference equations, special methods have been developed which, in one way or another, take into account special features of the problem, and which allow the solution to be found using less work than via the general methods. This work is an extension of the book Difference M ethod3 for the Solution of Elliptic Equation3 by A. A. Samarskii and V. B. Andreev which considered a whole set of questions connected with difference approximations, the con struction of difference operators, and estimation of the ~onvergence rate of difference schemes for typical elliptic boundary-value problems. Here we consider only solution methods for difference equations. The book in fact consists of two volumes.

Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - The finite-difference solution of mathematical-physics differential equations is carried out in two stages: 1) the writing of the difference scheme (a differ ence approximation to the differential equation on a grid), 2) the computer solution of the difference equations, which are written in the form of a high order system of linear algebraic equations of special form (ill-conditioned, band-structured). Application of general linear algebra methods is not always appropriate for such systems because of the need to store a large volume of information, as well as because of the large amount of work required by these methods. For the solution of difference equations, special methods have been developed which, in one way or another, take into account special features of the problem, and which allow the solution to be found using less work than via the general methods. This work is an extension of the book Difference M ethod3 for the Solution of Elliptic Equation3 by A. A. Samarskii and V. B. Andreev which considered a whole set of questions connected with difference approximations, the con struction of difference operators, and estimation of the ~onvergence rate of difference schemes for typical elliptic boundary-value problems. Here we consider only solution methods for difference equations. The book in fact consists of two volumes.

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Hardcover. Revised Edition. Devoted to the solution of differential equations arising in Mathematical Physics, text in English. Vol. I Direct Methods, 242 pages; Vol. II Iterative Methods, 502 pages. German ISBN 3764322780. Shipping may be extra for this large heavy set; please inquire.; Two Volume Set; 6 3/4 x 9 1/2 " Near Fine in Near Fine dust jacket.

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