Numerical Linear Algebra [[electronic resource] ] : A Concise Introduction with MATLAB and Julia / / by Folkmar Bornemann

• Autore: Bornemann Folkmar
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018
• Edizione: 1st ed. 2018.
• Descrizione fisica: 1 online resource (X, 153 p. 1 illus. in color.)
• Disciplina: 512.5
• Soggetto topico: Matrix theory; Algebra; Numerical analysis; Linear and Multilinear Algebras, Matrix Theory; Numerical Analysis
• Nota di contenuto: Intro -- Preface -- Student's Laboratory -- Contents -- I: Computing with Matrices -- 1 What is Numerical Analysis? -- 2 Matrix Calculus -- 3 MATLAB -- 4 Execution Times -- 5 Triangular Matrices -- 6 Unitary Matrices -- II: Matrix Factorization -- 7 Triangular Decomposition -- 8 Cholesky Decomposition -- 9 QR Decomposition -- III: Error Analysis -- 10 Error Measures -- 11 Conditioning of a Problem -- 12 Machine Numbers -- 13 Stability of an Algorithm -- 14 Three Exemplary Error Analyses -- 15 Error Analysis of Linear Systems of Equations -- IV: Least Squares -- 16 Normal Equation -- 17 Orthogonalization -- V: Eigenvalue Problems -- 18 Basic Concepts -- 19 Perturbation Theory -- 20 Power Iteration -- 21 QR Algorithm -- Appendix -- A MATLAB: A Very Short Introduction -- General Commands -- Matrices -- Functions -- Control Flow -- Logic Functions -- Componentwise Operations -- B Julia: A Modern Alternative to MATLAB -- C Norms: Recap and Supplement -- D The Householder Method for QR Decomposition -- E For the Curious, the Connoisseur, and the Capable -- Model Backwards Analysis of Iterative Refinement -- Global Convergence of the QR Algorithm without Shifts -- Local Convergence of the QR Algorithm with Shifts -- A Stochastic Upper Bound of the Spectral Norm -- F More Exercises -- Computer Matrices -- Matrix Factorization -- Error Analysis -- Least Squares -- Elgenvalue Problems -- Notation -- Index.
• Sommario/riassunto: This book offers an introduction to the algorithmic-numerical thinking using basic problems of linear algebra. By focusing on linear algebra, it ensures a stronger thematic coherence than is otherwise found in introductory lectures on numerics. The book highlights the usefulness of matrix partitioning compared to a component view, leading not only to a clearer notation and shorter algorithms, but also to significant runtime gains in modern computer architectures. The algorithms and accompanying numerical examples are given in the programming environment MATLAB, and additionally – in an appendix – in the future-oriented, freely accessible programming language Julia. This book is suitable for a two-hour lecture on numerical linear algebra from the second semester of a bachelor's degree in mathematics.
• Titolo autorizzato: Numerical Linear Algebra
• ISBN: 3-319-74222-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910300112803321
• Lo trovi qui: Univ. Federico II
• Serie: Springer Undergraduate Mathematics Series, . 1615-2085