Preface Part I. Fundamental: 1. Matrix-vector multiplication 2. Orthogonal vectors and matrices 3. Norms 4. The singular value decomposition 5. More on the SVD Part II. QR Factorization and Least Squares: 6. Projectors 7. QR factorization 8. Gram-Schmidt orthogonalization 9. MATLAB 10. Householder triangularization 11. Least squares problems Part III. Conditioning and Stability: 12. Conditioning and condition numbers 13. Floating point arithmetic 14. Stability 15. More on stability 16. Stability of householder triangularization 17. Stability of back substitution 18. Conditioning of least squares problems 19. Stability of least squares algorithms Part IV. Systems of Equations: 20. Gaussian elimination 21. Pivoting 22. Stability of Gaussian elimination 23. Cholesky factorization Part V. Eigenvalues: 24. Eigenvalue problems 25. Overview of Eigenvalue algorithms 26. Reduction to Hessenberg or tridiagonal form 27. Rayleigh quotient, inverse iteration 28. QR algorithm without shifts 29. QR algorithm with shifts 30. Other Eigenvalue algorithms 31. Computing the SVD Part VI. Iterative Methods: 32. Overview of iterative methods 33. The Arnoldi iteration 34. How Arnoldi locates Eigenvalues 35. GMRES 36. The Lanczos iteration 37. From Lanczos to Gauss quadrature 38. Conjugate gradients 39. Biorthogonalization methods 40. Preconditioning Appendix Notes Bibliography Index.
Preface Part I. Fundamental: 1. Matrix-vector multiplication 2. Orthogonal vectors and matrices 3. Norms 4. The singular value decomposition 5. More on the SVD Part II. QR Factorization and Least Squares: 6. Projectors 7. QR factorization 8. Gram-Schmidt orthogonalization 9. MATLAB 10. Householder triangularization 11. Least squares problems Part III. Conditioning and Stability: 12. Conditioning and condition numbers 13. Floating point arithmetic 14. Stability 15. More on stability 16. Stability of householder triangularization 17. Stability of back substitution 18. Conditioning of least squares problems 19. Stability of least squares algorithms Part IV. Systems of Equations: 20. Gaussian elimination 21. Pivoting 22. Stability of Gaussian elimination 23. Cholesky factorization Part V. Eigenvalues: 24. Eigenvalue problems 25. Overview of Eigenvalue algorithms 26. Reduction to Hessenberg or tridiagonal form 27. Rayleigh quotient, inverse iteration 28. QR algorithm without shifts 29. QR algorithm with shifts 30. Other Eigenvalue algorithms 31. Computing the SVD Part VI. Iterative Methods: 32. Overview of iterative methods 33. The Arnoldi iteration 34. How Arnoldi locates Eigenvalues 35. GMRES 36. The Lanczos iteration 37. From Lanczos to Gauss quadrature 38. Conjugate gradients 39. Biorthogonalization methods 40. Preconditioning Appendix Notes Bibliography Index.
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