Numerical Linear Algebra - 북프라이스

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· 제목 : Numerical Linear Algebra (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 대수학 > 선형대수학
· ISBN : 9780898713619
· 쪽수 : 184쪽
· 출판일 : 1997-06-01

Preface
Acknowledgments
Part I: Fundamentals. Lecture 1: Matrix-Vector Multiplication
Lecture 2: Orthogonal Vectors and Matrices
Lecture 3: Norms
Lecture 4: The Singular Value Decomposition
Lecture 5: More on the SVD
Part II: QR Factorization and Least Squares. Lecture 6: Projectors
Lecture 7: QR Factorization
Lecture 8: Gram-Schmidt Orthogonalization
Lecture 9: MATLAB
Lecture 10: Householder Triangularization
Lecture 11: Least Squares Problems
Part III: Conditioning and Stability. Lecture 12: Conditioning and Condition Numbers
Lecture 13: Floating Point Arithmetic
Lecture 14: Stability
Lecture 15: More on Stability
Lecture 16: Stability of Householder Triangularization
Lecture 17: Stability of Back Substitution
Lecture 18: Conditioning of Least Squares Problems
Lecture 19: Stability of Least Squares Algorithms
Part IV: Systems of Equations. Lecture 20: Gaussian Elimination
Lecture 21: Pivoting
Lecture 22: Stability of Gaussian Elimination
Lecture 23: Cholesky Factorization
Part V: Eigenvalues. Lecture 24: Eigenvalue Problems
Lecture 25: Overview of Eigenvalue Algorithms
Lecture 26: Reduction to Hessenberg or Tridiagonal Form
Lecture 27: Rayleigh Quotient, Inverse Iteration
Lecture 28: QR Algorithm without Shifts
Lecture 29: QR Algorithm with Shifts
Lecture 30: Other Eigenvalue Algorithms
Lecture 31: Computing the SVD
Part VI: Iterative Methods. Lecture 32: Overview of Iterative Methods
Lecture 33: The Arnoldi Iteration
Lecture 34: How Arnoldi Locates Eigenvalues
Lecture 35: GMRES
Lecture 36: The Lanczos Iteration
Lecture 37: From Lanczos to Gauss Quadrature
Lecture 38: Conjugate Gradients
Lecture 39: Biorthogonalization Methods
Lecture 40: Preconditioning
Appendix: The Definition of Numerical Analysis
Notes
Bibliography
Index.