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Introduction to numerical analysis / J. Stoer (1993)

Public Titre : Introduction to numerical analysis Type de document : Guide/Manuel Auteurs : J. Stoer, Auteur ; R. Bulirsch, Auteur ; R. Bartels, Traducteur ; W. Gautschi, Traducteur ; C. Witzgall, Traducteur Mention d'édition : 2 Editeur : Berlin, Heidelberg, Vienne, New York, ... : Springer Année de publication : 1993 Collection : Texts in applied mathematics num. 12 Importance : 660 p. Format : 16 x 24 cm ISBN/ISSN/EAN : 978-0-387-97878-9 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse numérique [Termes IGN] analyse numérique [Termes IGN] équation différentielle [Termes IGN] équation linéaire [Termes IGN] interpolation [Termes IGN] itération [Termes IGN] modèle par fonctions rationnelles [Termes IGN] transformation rapide de Fourier [Termes IGN] valeur propre Note de contenu : 1 Error Analysis 1.1 Representation of Numbers 1.2 Roundoff Errors and Floating-Point Arithmetic 1.3 Error Propagation 1.4 Examples 1.5 Interval Arithmetic ; Statistical Roundoff Estimation Exercises for Chapter 1 References for Chapter 1 2 Interpolation 2.1 Interpolation by Polynomials 2.2 Interpolation by Rational Functions 2.3 Trigonometric Interpolation 2.4 Interpolation by Spline Functions Exercises for Chapter 2 References for Chapter 2 3 Topics in Integration 3.1 The Integration Formulas of Newton and Cotes 3.2 Peano's Error Representation 3.3 The Euler-Maclaurin Summation Formula 3.4 Integrating by Extrapolation 3.5 About Extrapolation Methods 3.6 Gaussian Integration Methods 3.7 Integrals with Singularities Exercises for Chapter 3 References for Chapter 3 4 Systems of Linear Equations 4.1 Gaussian Elimination. The Triangular Decomposition of a Matrix 4.2 The Gauss-Jordan Algorithm 4.3 The Cholesky Decomposition 4.4 Error Bounds 4.5 Roundoff-Error Analysis for Gaussian Elimination 4.6 Roundoff Errors in Solving Triangular Systems 4.7 Orthogonalization Techniques of Householder and Gram-Schmidt 4.8 Data Fitting 4.9 Modification Techniques for Matrix Decompositions 4.10 The Simplex Method 4.11 Phase One of the Simplex Method Appendix to Chapter 4 4.A Elimination Methods for Sparse Matrices Exercises for Chapter 4 References for Chapter 4 5 Finding Zeros and Minimum Points by Iterative Methods 5.1 The Development of Iterative Methods 5.2 General Convergence Theorems 5.3 The Convergence of Newton's Method in Several Variables 5.4 A Modified Newton Method 5.5 Roots of Polynomials. Application of Newton's Method 5.6 Sturm Sequences and Bisection Methods 5.7 Bairstow's Method 5.8 The Sensitivity of Polynomial Roots 5.9 Interpolation Methods for Determining Roots 5.10 The A'-Method of Aitken 5.11 Minimization Problems without Constraints Exercises for Chapter 5 References for Chapter 5 6 Eigenvalue Problems 6.0 Introduction 6.1 Basic Facts on Eigenvalues 6.2 The Jordan Normal Form of a Matrix 6.3 The Frobenius Normal Form of a Matrix 6.4 The Schur Normal Form of a Matrix ; Hermitian and Normal Matrices ; Singular Values of Matrices 6.5 Reduction of Matrices to Simpler Form 6.6 Methods for Determining the Eigenvalues and Eigenvectors 6.7 Computation of the Singular Values of a Matrix 6.8 Generalized Eigenvalue Problems 6.9 Estimation of Eigenvalues Exercises for Chapter 6 References for Chapter 6 7 Ordinary Differential Equations 7.0 Introduction 7.1 Some Theorems from the Theory of Ordinary Differential Equations 7.2 Initial-Value Problems 7.3 Boundary-Value Problems 7.4 Difference Methods 7.5 Variational Methods 7.6 Comparison of the Methods for Solving Boundary-Value Problems for Ordinary Differential Equations 7.7 Variational Methods for Partial Differential Equations. The Finite-Element Method Exercises for Chapter 7 References for Chapter 7 8 Iterative Methods for the Solution of Large Systems of Linear Equations. Some Further Methods 8.0 Introduction 8.1 General Procedures for the Construction of Iterative Methods 8.2 Convergence Theorems 8.3 Relaxation Methods 8.4 Applications to Difference Methods - An Example 8.5 Block Iterative Methods 8.6 The ADI-Method of Peaceman and Rachford 8.7 The Conjugate-Gradient Method of Hestenes and Stiefel 8.8 The Algorithm of Buneman for the Solution of the Discretized Poisson Equation 8.9 Multigrid Methods 8.10 Comparison of Iterative Methods Exercises for Chapter 8 References for Chapter 8 Numéro de notice : 13031 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE Nature : Manuel de cours Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=46242