Numerical linear algebra : a concise introduction with MATLAB and Julia /
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| Author / Creator: | Bornemann, Folkmar, 1967- author. |
|---|---|
| Imprint: | Cham : Springer, 2018. |
| Description: | 1 online resource (x, 153 pages) : color illustrations |
| Language: | English |
| Series: | Springer Undergraduate Mathematics Series, 1615-2085 Springer undergraduate mathematics series, |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11543265 |
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| 100 | 1 | |a Bornemann, Folkmar, |d 1967- |e author. |0 http://id.loc.gov/authorities/names/n98039836 | |
| 245 | 1 | 0 | |a Numerical linear algebra : |b a concise introduction with MATLAB and Julia / |c Folkmar Bornemann. |
| 264 | 1 | |a Cham : |b Springer, |c 2018. | |
| 300 | |a 1 online resource (x, 153 pages) : |b color illustrations | ||
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| 490 | 1 | |a Springer Undergraduate Mathematics Series, |x 1615-2085 | |
| 520 | |a 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. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 650 | 0 | |a Algebras, Linear. |0 http://id.loc.gov/authorities/subjects/sh85003441 | |
| 650 | 0 | |a Mathematics. |0 http://id.loc.gov/authorities/subjects/sh85082139 | |
| 650 | 0 | |a Matrix theory. | |
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| 650 | 0 | |a Numerical analysis. |0 http://id.loc.gov/authorities/subjects/sh85093237 | |
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| 650 | 7 | |a Numerical analysis. |2 fast |0 (OCoLC)fst01041273 | |
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| 776 | 0 | 8 | |i Printed edition: |z 9783319742212 |
| 830 | 0 | |a Springer undergraduate mathematics series, |x 1615-2085 |0 http://id.loc.gov/authorities/names/n97070454 | |
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