Transcription of Iterative Methods for Sparse Linear Systems
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Iterative Methods for Sparse Linear Systems
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 .. 15. Reduction to the Diagonal Form .. 15. The Jordan Canonical Form .. 16. The Schur Canonical Form .. 17. Application to Powers of Matrices.
Iterative methods for solving general, large sparse linear systems have been gaining popularity in many areas of scientific computing. Until recently, direct solution methods
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