Numerical Linear Algebra pdf epub mobi txt 電子書下載2025

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出版者:SIAM: Society for Industrial and Applied Mathematics

作者:Lloyd N. Trefethen

出品人:

頁數:361

译者:

出版時間:1997-06-01

價格:USD 61.00

裝幀:Paperback

isbn號碼:9780898713619

叢書系列:

圖書標籤:

綫性代數
數學
機器學習
Mathematics
數值綫代
Algebra
算法
Linear
數值綫性代數
矩陣計算
數值分析
綫性方程組
特徵值問題
迭代法
QR分解
SVD
誤差分析
科學計算

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具體描述

Numerical Linear Algebra is a concise, insightful, and elegant introduction to the field of numerical linear algebra.

著者簡介

圖書目錄

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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