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Informationen zum Autor DAVID S. WATKINS, PhD , is Professor in the Department of Mathematics at Washington State University. He has published more than 100 articles in his areas of research interest, which include numerical linear algebra, numerical analysis, and scientific computing. Klappentext This new, modernized edition provides a clear and thorough introduction to matrix computations,a key component of scientific computingRetaining the accessible and hands-on style of its predecessor, Fundamentals of Matrix Computations, Third Edition thoroughly details matrix computations and the accompanying theory alongside the author's useful insights. The book presents the most important algorithms of numerical linear algebra and helps readers to understand how the algorithms are developed and why they work.Along with new and updated examples, the Third Edition features:* A novel approach to Francis' QR algorithm that explains its properties without reference to the basic QR algorithm* Application of classical Gram-Schmidt with reorthogonalization* A revised approach to the derivation of the Golub-Reinsch SVD algorithm* New coverage on solving product eigenvalue problems* Expanded treatment of the Jacobi-Davidson method* A new discussion on stopping criteria for iterative methods for solving linear equationsThroughout the book, numerous new and updated exercises--ranging from routine computations and verifications to challenging programming and proofs--are provided, allowing readers to immediately engage in applying the presented concepts. The new edition also incorporates MATLAB(r) to solve real-world problems in electrical circuits, mass-spring systems, and simple partial differential equations, and an index of MATLAB(r) terms assists readers with understanding the basic concepts related to the software.Fundamentals of Matrix Computations, Third Edition is an excellent book for courses on matrix computations and applied numerical linear algebra at the upper-undergraduate and graduate level. The book is also a valuable resource for researchers and practitioners working in the fields of engineering and computer science who need to know how to solve problems involving matrix computations. Zusammenfassung * This Third Edition explains how to perform matrix computations efficiently and accurately by providing a detailed introduction to the fundamental ideas of numerical linear algebra and utilizes MATLAB(R) to perform elaborate computational experiments. Inhaltsverzeichnis Preface. Acknowledgments. 1 Gaussian Elimination and Its Variants. 1.1 Matrix Multiplication. 1.2 Systems of Linear Equations. 1.3 Triangular Systems. 1.4 Positive Definite Systems; Cholesky Decomposition. 1.5 Banded Positive Definite Systems. 1.6 Sparse Positive Definite Systems. 1.7 Gaussian Elimination and the LU Decomposition. 1.8 Gaussain Elimination and Pivoting. 1.9 Sparse Gaussian Elimination. 2 Sensitivity of Linear Systems. 2.1 Vector and Matrix Norms. 2.2 Condition Numbers. 2.3 Perturbing the Coefficient Matrix. 2.4 A Posteriori Error Analysis Using the Residual. 2.5 Roundoff Errors; Backward Stability. 2.6 Propagation of Roundoff Errors. 2.7 Backward Error Analysis of Gaussian Elimination. 2.8 Scaling. 2.9 Componentwise Sensitivity Analysis. 3 The Least Squares Problem. 3.1 The Discrete Square Problem. 3.2 Orthogonal Matrices, Rotators and Reflectors. 3.3 Solution of the Least Squares Problem. 3.4 The Gram-Schmidt Process. 3.5 Geometric Approach. 3.6 Updating the QR Decomposition. 4 The Singular Value Decomposition. 4.1 Introduction. 4.2 Some Basic Applications of Singular Values. 4.3 The SVD and the Least Squares Problem. 4.4 Sensitivity...
