Numerical Linear Algebra pdf epub mobi txt 电子书下载 2025

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出版者:SIAM: Society for Industrial and Applied Mathematics

作者:Lloyd N. Trefethen

出品人:

页数:361

译者:

出版时间:1997-06-01

价格:USD 61.00

装帧:Paperback

isbn号码:9780898713619

丛书系列:

图书标签:

线性代数
数学
机器学习
Mathematics
数值线代
Algebra
算法
Linear
数值线性代数
矩阵计算
数值分析
线性方程组
特征值问题
迭代法
QR分解
SVD
误差分析
科学计算

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具体描述

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

作者简介

目录信息

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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