{"product_id":"fundamentals-of-matrix-computations-isbn-9780470528334","title":"Fundamentals of Matrix Computations","description":"\u003cb\u003eThis new, modernized edition provides a clear and thorough introduction to matrix computations,a key component of scientific computing\u003c\/b\u003e  \u003cp\u003eRetaining the accessible and hands-on style of its predecessor, \u003ci\u003eFundamentals of Matrix Computations\u003c\/i\u003e, 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.\u003c\/p\u003e \u003cp\u003eAlong with new and updated examples, the \u003ci\u003eThird Edition\u003c\/i\u003e features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA novel approach to Francis' QR algorithm that explains its properties without reference to the basic QR algorithm\u003c\/li\u003e \u003cli\u003eApplication of classical Gram-Schmidt with reorthogonalization\u003c\/li\u003e \u003cli\u003eA revised approach to the derivation of the Golub-Reinsch SVD algorithm\u003c\/li\u003e \u003cli\u003eNew coverage on solving product eigenvalue problems\u003c\/li\u003e \u003cli\u003eExpanded treatment of the Jacobi-Davidson method\u003c\/li\u003e \u003cli\u003eA new discussion on stopping criteria for iterative methods for solving linear equations\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThroughout 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 to solve real-world problems in electrical circuits, mass-spring systems, and simple partial differential equations, and an index of MATLAB terms assists readers with understanding the basic concepts related to the software.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eFundamentals of Matrix Computations\u003c\/i\u003e, 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.\u003c\/p\u003e  Preface.  \u003cp\u003eAcknowledgments.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Gaussian Elimination and Its Variants.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Matrix Multiplication.\u003c\/p\u003e \u003cp\u003e1.2 Systems of Linear Equations.\u003c\/p\u003e \u003cp\u003e1.3 Triangular Systems.\u003c\/p\u003e \u003cp\u003e1.4 Positive Definite Systems; Cholesky Decomposition.\u003c\/p\u003e \u003cp\u003e1.5 Banded Positive Definite Systems.\u003c\/p\u003e \u003cp\u003e1.6 Sparse Positive Definite Systems.\u003c\/p\u003e \u003cp\u003e1.7 Gaussian Elimination and the \u003ci\u003eLU\u003c\/i\u003e Decomposition.\u003c\/p\u003e \u003cp\u003e1.8 Gaussain Elimination and Pivoting.\u003c\/p\u003e \u003cp\u003e1.9 Sparse Gaussian Elimination.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Sensitivity of Linear Systems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Vector and Matrix Norms.\u003c\/p\u003e \u003cp\u003e2.2 Condition Numbers.\u003c\/p\u003e \u003cp\u003e2.3 Perturbing the Coefficient Matrix.\u003c\/p\u003e \u003cp\u003e2.4 A Posteriori Error Analysis Using the Residual.\u003c\/p\u003e \u003cp\u003e2.5 Roundoff Errors; Backward Stability.\u003c\/p\u003e \u003cp\u003e2.6 Propagation of Roundoff Errors.\u003c\/p\u003e \u003cp\u003e2.7 Backward Error Analysis of Gaussian Elimination.\u003c\/p\u003e \u003cp\u003e2.8 Scaling.\u003c\/p\u003e \u003cp\u003e2.9 Componentwise Sensitivity Analysis.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 The Least Squares Problem.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Discrete Square Problem.\u003c\/p\u003e \u003cp\u003e3.2 Orthogonal Matrices, Rotators and Reflectors.\u003c\/p\u003e \u003cp\u003e3.3 Solution of the Least Squares Problem.\u003c\/p\u003e \u003cp\u003e3.4 The Gram-Schmidt Process.\u003c\/p\u003e \u003cp\u003e3.5 Geometric Approach.\u003c\/p\u003e \u003cp\u003e3.6 Updating the QR Decomposition.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 The Singular Value Decomposition.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction.\u003c\/p\u003e \u003cp\u003e4.2 Some Basic Applications of Singular Values.\u003c\/p\u003e \u003cp\u003e4.3 The SVD and the Least Squares Problem.\u003c\/p\u003e \u003cp\u003e4.4 Sensitivity of the Least Squares Problem.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Eigenvalues and Eigenvectors I.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Systems of Differential Equations.\u003c\/p\u003e \u003cp\u003e5.2 Basic Facts.\u003c\/p\u003e \u003cp\u003e5.3 The Power Method and Some Simple Extensions.\u003c\/p\u003e \u003cp\u003e5.4 Similarity Transforms.\u003c\/p\u003e \u003cp\u003e5.5 Reduction to Hessenberg and Tridiagonal Forms.\u003c\/p\u003e \u003cp\u003e5.6 Francis's Algorithm.\u003c\/p\u003e \u003cp\u003e5.7 Use of Francis's Algorithm to Calculate Eigenvectors.\u003c\/p\u003e \u003cp\u003e5.8 The SVD Revisted.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Eigenvalues and Eigenvectors II.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Eigenspaces and Invariant Subspaces.\u003c\/p\u003e \u003cp\u003e6.2 Subspace Iteration and Simultaneous Iteration.\u003c\/p\u003e \u003cp\u003e6.3 Krylov Subspaces and Francis's Algorithm.\u003c\/p\u003e \u003cp\u003e6.4 Large Sparse Eigenvalue Problems.\u003c\/p\u003e \u003cp\u003e6.5 Implicit Restarts.\u003c\/p\u003e \u003cp\u003e6.6 The Jacobi-Davidson and Related Algorithms.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Eigenvalues and Eigenvectors III.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Sensitivity of Eigenvalues and Eigenvectors.\u003c\/p\u003e \u003cp\u003e7.2 Methods for the Symmetric Eigenvalue Problem.\u003c\/p\u003e \u003cp\u003e7.3 Product Eigenvalue Problems.\u003c\/p\u003e \u003cp\u003e7.4 The Generalized Eigenvalue Problem.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Iterative Methods for Linear Systems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 A Model Problem.\u003c\/p\u003e \u003cp\u003e8.2 The Classical Iterative Methods.\u003c\/p\u003e \u003cp\u003e8.3 Convergence of Iterative Methods.\u003c\/p\u003e \u003cp\u003e8.4 Descent Methods; Steepest Descent.\u003c\/p\u003e \u003cp\u003e8.5 On Stopping Criteria.\u003c\/p\u003e \u003cp\u003e8.6 Preconditioners.\u003c\/p\u003e \u003cp\u003e8.7 The Conjugate-Gradient Method.\u003c\/p\u003e \u003cp\u003e8.8 Derivation of the CG Algorithm.\u003c\/p\u003e \u003cp\u003e8.9 Convergence of the CG Algorithm.\u003c\/p\u003e \u003cp\u003e8.10 Indefinite and Nonsymmetric Problems.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e \u003cp\u003eIndex of MATLAB Terms.\u003c\/p\u003e \u003cb\u003eDAVID S. WATKINS, PhD\u003c\/b\u003e, 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.  \u003cb\u003eThis new, modernized edition provides a clear and thorough introduction to matrix computations, a key component of scientific computing\u003c\/b\u003e  \u003cp\u003eRetaining the accessible and hands-on style of its predecessor, \u003ci\u003eFundamentals of Matrix Computations, Third Edition\u003c\/i\u003e 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.\u003c\/p\u003e \u003cp\u003eAlong with new and updated examples, the \u003ci\u003eThird Edition\u003c\/i\u003e features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA novel approach to Francis' QR algorithm that explains its properties without reference to the basic QR algorithm\u003c\/li\u003e \u003cli\u003eApplication of classical Gram-Schmidt with reorthogonalization\u003c\/li\u003e \u003cli\u003eA revised approach to the derivation of the Golub-Reinsch SVD algorithm\u003c\/li\u003e \u003cli\u003eNew coverage on solving product eigenvalue problems\u003c\/li\u003e \u003cli\u003eExpanded treatment of the Jacobi-Davidson method\u003c\/li\u003e \u003cli\u003eA new discussion on stopping criteria for iterative methods for solving linear equations\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThroughout 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 to solve real-world problems in electrical circuits, mass-spring systems, and simple partial differential equations, and an index of MATLAB terms assists readers with understanding the basic concepts related to the software.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eFundamentals of Matrix Computations, Third Edition\u003c\/i\u003e 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989261369573,"sku":"NP9780470528334","price":145.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470528334.jpg?v=1761783422","url":"https:\/\/k12savings.com\/products\/fundamentals-of-matrix-computations-isbn-9780470528334","provider":"K12savings","version":"1.0","type":"link"}