| Autore |
Bornemann Folkmar
|
| Edizione | [1st ed. 2018.] |
| Pubbl/distr/stampa |
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018
|
| Descrizione fisica |
1 online resource (X, 153 p. 1 illus. in color.)
|
| Disciplina |
512.5
|
| Collana |
Springer Undergraduate Mathematics Series
|
| Soggetto topico |
Matrix theory
Algebra
Numerical analysis
Linear and Multilinear Algebras, Matrix Theory
Numerical Analysis
|
| ISBN |
3-319-74222-1
|
| Formato |
Materiale a stampa  |
| Livello bibliografico |
Monografia |
| Lingua di pubblicazione |
eng
|
| 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.
|
| Record Nr. | UNINA-9910300112803321 |
Info
Numerical Linear Algebra [[electronic resource] ] : A Concise Introduction with MATLAB and Julia / / by Folkmar Bornemann
