Numerical Linear Algebra with Applications (Record no. 2089)
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| fixed length control field | 08293nam a22001817a 4500 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240827103735.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240221b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780123944351 (HB) |
| 041 ## - LANGUAGE CODE | |
| Language code of text/sound track or separate title | eng |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.5 |
| Item number | FOR |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | William Ford |
| 245 ## - TITLE STATEMENT | |
| Title | Numerical Linear Algebra with Applications |
| Remainder of title | Using MATLAB |
| Statement of responsibility, etc. | William Ford |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. | |
| Place of publication, distribution, etc. | UK |
| Name of publisher, distributor, etc. | Academic Press |
| Date of publication, distribution, etc. | 2015 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Page number | XXVI, 602 p |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Title | Chapter 1: Matrices<br/>Abstract<br/>1.1 Matrix Arithmetic<br/>1.2 Linear Transformations<br/>1.3 Powers of Matrices<br/>1.4 Nonsingular Matrices<br/>1.5 The Matrix Transpose and Symmetric Matrices<br/>1.6 Chapter Summary<br/>1.7 Problems<br/>Chapter 2: Linear Equations<br/>Abstract<br/>2.1 Introduction to Linear Equations<br/>2.2 Solving Square Linear Systems<br/>2.3 Gaussian Elimination<br/>2.4 Systematic Solution of Linear Systems<br/>2.5 Computing the Inverse<br/>2.6 Homogeneous Systems<br/>2.7 Application: A Truss<br/>2.8 Application: Electrical Circuit<br/>2.9 Chapter Summary<br/>2.10 Problems<br/>Chapter 3: Subspaces<br/>Abstract<br/>3.1 Introduction<br/>3.2 Subspaces of n<br/>3.3 Linear Independence<br/>3.4 Basis of a Subspace<br/>3.5 The Rank of a Matrix<br/>3.6 Chapter summary<br/>3.7 Problems<br/>Chapter 4: Determinants<br/>Abstract<br/>4.1 Developing the Determinant of A 2 × 2 and A 3 × 3 matrix<br/>4.2 Expansion by Minors<br/>4.3 Computing a Determinant Using Row Operations<br/>4.4 Application: Encryption<br/>4.5 Chapter Summary<br/>4.6 Problems<br/>Chapter 5: Eigenvalues and Eigenvectors<br/>Abstract<br/>5.1 Definitions and Examples<br/>5.2 Selected Properties of Eigenvalues and Eigenvectors<br/>5.3 Diagonalization<br/>5.4 Applications<br/>5.5 Computing Eigenvalues and Eigenvectors Using Matlab<br/>5.6 Chapter Summary<br/>5.7 Problems<br/>Chapter 6: Orthogonal Vectors and Matrices<br/>Abstract<br/>6.1 Introduction<br/>6.2 The Inner Product<br/>6.3 Orthogonal Matrices<br/>6.4 Symmetric Matrices and Orthogonality<br/>6.5 The L2 inner product<br/>6.6 The Cauchy-Schwarz Inequality<br/>6.7 Signal Comparison<br/>6.8 Chapter Summary<br/>6.9 Problems<br/>Chapter 7: Vector and Matrix Norms<br/>Abstract<br/>7.1 Vector Norms<br/>7.3 Submultiplicative Matrix Norms<br/>7.4 Computing the Matrix 2-Norm<br/>7.5 Properties of the Matrix 2-Norm<br/>7.6 Chapter Summary<br/>7.7 Problems<br/>Chapter 8: Floating Point Arithmetic<br/>Abstract<br/>8.1 Integer Representation<br/>8.2 Floating-Point Representation<br/>8.3 Floating-Point Arithmetic<br/>8.4 Minimizing Errors<br/>8.5 Chapter summary<br/>8.6 Problems<br/>Chapter 9: Algorithms<br/>Abstract<br/>9.1 Pseudocode Examples<br/>9.2 Algorithm Efficiency<br/>9.3 The Solution to Upper and Lower Triangular Systems<br/>9.4 The Thomas Algorithm<br/>9.5 Chapter Summary<br/>9.6 Problems<br/>Chapter 10: Conditioning of Problems and Stability of Algorithms<br/>Abstract<br/>10.1 Why do we need numerical linear algebra?<br/>10.2 Computation error<br/>10.3 Algorithm stability<br/>10.4 Conditioning of a problem<br/>10.5 Perturbation analysis for solving a linear system<br/>10.6 Properties of the matrix condition number<br/>10.7 Matlab computation of a matrix condition number<br/>10.8 Estimating the condition number<br/>10.9 Introduction to perturbation analysis of eigenvalue problems<br/>10.10 Chapter summary<br/>10.11 Problems<br/>Chapter 11: Gaussian Elimination and the LU Decomposition<br/>Abstract<br/>11.1 LU Decomposition<br/>11.2 Using LU to Solve Equations<br/>11.3 Elementary Row Matrices<br/>11.4 Derivation of the LU Decomposition<br/>11.5 Gaussian Elimination with Partial Pivoting<br/>11.6 Using the LU Decomposition to Solve Axi=bi,1≤i≤k<br/>11.7 Finding A–1<br/>11.8 Stability and Efficiency of Gaussian Elimination<br/>11.9 Iterative Refinement<br/>11.10 Chapter Summary<br/>11.11 Problems<br/>Chapter 12: Linear System Applications<br/>Abstract<br/>12.1 Fourier Series<br/>12.2 Finite Difference Approximations<br/>12.3 Least-Squares Polynomial Fitting<br/>12.4 Cubic Spline Interpolation<br/>12.5 Chapter Summary<br/>12.6 Problems<br/>Chapter 13: Important Special Systems<br/>Abstract<br/>13.1 Tridiagonal Systems<br/>13.2 Symmetric Positive Definite Matrices<br/>13.3 The Cholesky Decomposition<br/>13.4 Chapter Summary<br/>13.5 Problems<br/>Chapter 14: Gram-Schmidt Orthonormalization<br/>Abstract<br/>14.1 The Gram-Schmidt Process<br/>14.2 Numerical Stability of the Gram-Schmidt Process<br/>14.3 The QR Decomposition<br/>14.3.1 Efficiency<br/>14.3.2 Stability<br/>14.4 Applications of The QR Decomposition<br/>14.5 Chapter Summary<br/>14.6 Problems<br/>Chapter 15: The Singular Value Decomposition<br/>Abstract<br/>15.1 The SVD Theorem<br/>15.2 Using the SVD to Determine Properties of a Matrix<br/>15.3 SVD and Matrix Norms<br/>15.4 Geometric Interpretation of the SVD<br/>15.5 Computing the SVD Using MATLAB<br/>15.6 Computing A–1<br/>15.7 Image Compression Using the SVD<br/>15.8 Final Comments<br/>15.9 Chapter Summary<br/>15.10 Problems<br/>Chapter 16: Least-Squares Problems<br/>Abstract<br/>16.1 Existence and Uniqueness of Least-Squares Solutions<br/>16.2 Solving Overdetermined Least-Squares Problems<br/>16.3 Conditioning of Least-Squares Problems<br/>16.4 Rank-Deficient Least-Squares Problems<br/>16.5 Underdetermined Linear Systems<br/>16.6 Chapter Summary<br/>16.7 Problems<br/>Chapter 17: Implementing the QR Decomposition<br/>Abstract<br/>17.1 Review of the QR Decomposition Using Gram-Schmidt<br/>17.2 Givens Rotations<br/>17.3 Creating a Sequence of Zeros in a Vector Using Givens Rotations<br/>17.4 Product of a Givens Matrix with a General Matrix<br/>17.5 Zeroing-Out Column Entries in a Matrix Using Givens Rotations<br/>17.6 Accurate Computation of the Givens Parameters<br/>17.7 THe Givens Algorithm for the QR Decomposition<br/>17.8 Householder Reflections<br/>17.9 Computing the QR Decomposition Using Householder Reflections<br/>17.10 Chapter Summary<br/>17.11 Problems<br/>Chapter 18: The Algebraic Eigenvalue Problem<br/>Abstract<br/>18.1 Applications of The Eigenvalue Problem<br/>18.2 Computation of Selected Eigenvalues and Eigenvectors<br/>18.3 The Basic QR Iteration<br/>18.4 Transformation to Upper Hessenberg Form<br/>18.5 The Unshifted Hessenberg QR Iteration<br/>18.6 The Shifted Hessenberg QR Iteration<br/>18.7 Schur's Triangularization<br/>18.8 The Francis Algorithm<br/>18.9 Computing Eigenvectors<br/>18.10 Computing Both Eigenvalues and Their Corresponding Eigenvectors<br/>18.11 Sensitivity of Eigenvalues to Perturbations<br/>18.12 Chapter Summary<br/>18.13 Problems<br/>Chapter 19: The Symmetric Eigenvalue Problem<br/>Abstract<br/>19.1 The Spectral Theorem and Properties of A Symmetric Matrix<br/>19.2 The Jacobi Method<br/>19.3 The Symmetric QR Iteration Method<br/>19.4 The Symmetric Francis Algorithm<br/>19.5 The Bisection Method<br/>19.6 The Divide-And-Conquer Method<br/>19.7 Chapter Summary<br/>19.8 Problems<br/>Chapter 20: Basic Iterative Methods<br/>Abstract<br/>20.1 Jacobi Method<br/>20.2 The Gauss-Seidel Iterative Method<br/>20.3 The Sor Iteration<br/>20.4 Convergence of the Basic Iterative Methods<br/>20.5 Application: Poisson's Equation<br/>20.6 Chapter Summary<br/>20.7 Problems<br/>Chapter 21: Krylov Subspace Methods<br/>Abstract<br/>21.1 Large, Sparse Matrices<br/>21.2 The CG Method<br/>21.3 Preconditioning<br/>21.4 Preconditioning For CG<br/>21.5 Krylov Subspaces<br/>21.6 The Arnoldi Method<br/>21.16.1 An Alternative Formulation of the Arnoldi Decomposition<br/>21.7 GMRES<br/>21.8 The Symmetric Lanczos Method<br/>21.9 The Minres Method<br/>21.10 Comparison of Iterative Methods<br/>21.11 Poisson's Equation Revisited<br/>21.12 The Biharmonic Equation<br/>21.13 Chapter Summary<br/>21.14 Problems<br/>Chapter 22: Large Sparse Eigenvalue Problems<br/>Abstract<br/>22.1 The Power Method<br/>22.2 Eigenvalue Computation Using the Arnoldi Process<br/>22.3 The Implicitly Restarted Arnoldi Method<br/>22.4 Eigenvalue Computation Using the Lanczos Process<br/>22.5 Chapter Summary<br/>22.6 Problems<br/>Chapter 23: Computing the Singular Value Decomposition<br/>Abstract<br/>23.1 Development of the One-Sided Jacobi Method For Computing the Reduced Svd<br/>23.2 The One-Sided Jacobi Algorithm<br/>23.3 Transforming a Matrix to Upper-Bidiagonal Form<br/>23.4 Demmel and Kahan Zero-Shift QR Downward Sweep Algorithm<br/>23.5 Chapter Summary<br/>23.6 Problems |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. |
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| Dewey Decimal Classification | Non-fiction | IIITDM Kurnool | IIITDM Kurnool | General Stacks | 21.02.2024 | CBS Publisher & Distributers | 120.00 | COR/IN/24/10957 DT 2/2/2024 | 512.5 FOR | 0005440 | 21.02.2024 | 21.02.2024 | USD | Books | |||||||
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| Dewey Decimal Classification | Non-fiction | IIITDM Kurnool | IIITDM Kurnool | General Stacks | 27.08.2024 | Narendra Publishing House | 5984.00 | NPH/23-24/IN-00134 DATED 05/08/2 | 512.5 FOR | 0006211 | 27.08.2024 | 27.08.2024 | INR | Books | 9974.00 | 1 | |||||
| Dewey Decimal Classification | Non-fiction | IIITDM Kurnool | IIITDM Kurnool | General Stacks | 27.08.2024 | Narendra Publishing House | 5984.00 | NPH/23-24/IN-00134 DATED 05/08/2 | 512.5 FOR | 0006212 | 27.08.2024 | 27.08.2024 | INR | Books | 9974.00 | 2 | |||||
| Dewey Decimal Classification | Non-fiction | IIITDM Kurnool | IIITDM Kurnool | General Stacks | 27.08.2024 | Narendra Publishing House | 5984.00 | NPH/23-24/IN-00134 DATED 05/08/2 | 512.5 FOR | 0006213 | 27.08.2024 | 27.08.2024 | INR | Books | 9974.00 | 3 | |||||
| Dewey Decimal Classification | Non-fiction | IIITDM Kurnool | IIITDM Kurnool | General Stacks | 27.08.2024 | Narendra Publishing House | 5984.00 | NPH/23-24/IN-00134 DATED 05/08/2 | 512.5 FOR | 0006214 | 27.08.2024 | 27.08.2024 | INR | Books | 9974.00 | 4 |