Iterative Methods for Sparse Linear Systems

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Iterative Methods for Sparse Linear Systems Yousef Saad 6. 15 12. 4 9 5. 11 14 8. 2 10 3. 13 7. 1. Copyright c 2000 by Yousef Saad. S ECOND EDITION WITH CORRECTIONS . JANUARY 3 RD , 2000. . PREFACE xiii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv Suggestions for Teaching . . . . . . . . . . . . . . . . . . . . . . . . . xv 1 BACKGROUND IN Linear ALGEBRA 1. Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Square Matrices and Eigenvalues . . . . . . . . . . . . . . . . . . . . . 3. Types of Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Vector Inner Products and Norms . . . . . . . . . . . . . . . . . . . . . 6. Matrix Norms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Subspaces, Range, and Kernel . . . . . . . . . . . . . . . . . . . . . . . 9. Orthogonal Vectors and Subspaces . . . . . . . . . . . . . . . . . . . . 10. Canonical Forms of Matrices.

and the increased need for solving very large linear systems triggered a noticeable and rapid shift toward iterative techniques in many applications. This trend can be traced back to the 1960s and 1970s when two important develop-ments revolutionized solution methods for large linear systems. First was the realization

  Applications, System, Linear, Methods, Arsesp, Linear systems, Methods for sparse linear systems