Numerical linear algebra with applications using matlab
Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a first year graduate or advanced undergraduate course on numerical l...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
London, England :
Academic Press
2015.
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| Edición: | First edition |
| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009629193906719 |
Tabla de Contenidos:
- Front Cover; Numerical Linear Algebra with Applications; Copyright; Dedication; Contents; List of Figures; List of Algorithms; Preface; Matrices; Matrix Arithmetic; Matrix Product; The Trace; MATLAB Examples; Linear Transformations; Rotations; Powers of Matrices; Nonsingular Matrices; The Matrix Transpose and Symmetric Matrices; Chapter Summary; Problems; MATLAB Problems; Linear Equations; Introduction to Linear Equations; Solving Square Linear Systems; Gaussian Elimination; Upper-Triangular Form; Systematic Solution of Linear Systems; Computing the Inverse; Homogeneous Systems
- Application: A TrussApplication: Electrical Circuit; Chapter Summary; Problems; MATLAB Problems; Subspaces; Introduction; Subspaces of Rn; Linear Independence; Basis of a Subspace; The Rank of a Matrix; Chapter Summary; Problems; MATLAB Problems; Determinants; Developing the Determinant of a 2bold0mu mumu section2 and a 3bold0mu mumu section3 Matrix; Expansion by Minors; Computing a Determinant Using Row Operations; Application: Encryption; Chapter Summary; Problems; MATLAB Problems; Eigenvalues and Eigenvectors; Definitions and Examples; Selected Properties of Eigenvalues and Eigenvectors
- DiagonalizationPowers of Matrices; Applications; Electric Circuit; Irreducible Matrices; Ranking of Teams Using Eigenvectors; Computing Eigenvalues and Eigenvectors using MATLAB; Chapter Summary; Problems; MATLAB Problems; Orthogonal Vectors and Matrices; Introduction; The Inner Product; Orthogonal Matrices; Symmetric Matrices and Orthogonality; The L2 Inner Product; The Cauchy-Schwarz Inequality; Signal Comparison; Chapter Summary; Problems; MATLAB Problems; Vector and Matrix Norms; Vector Norms; Properties of the 2-Norm; Spherical Coordinates; Matrix Norms; The Frobenius Matrix Norm
- Induced Matrix NormsSubmultiplicative Matrix Norms; Computing the Matrix 2-Norm; Properties of the Matrix 2-Norm; Chapter Summary; Problems; MATLAB Problems; Floating Point Arithmetic; Integer Representation; Floating-Point Representation; Mapping from Real Numbers to Floating-Point Numbers; Floating-Point Arithmetic; Relative Error; Rounding Error Bounds; Addition; Multiplication; Matrix Operations; Minimizing Errors; Avoid Adding a Huge Number to a Small Number; Avoid Subtracting Numbers That Are Close; Chapter Summary; Problems; MATLAB Problems; Algorithms; Pseudocode Examples
- Inner Product of Two VectorsComputing the Frobenius Norm; Matrix Multiplication; Block Matrices; Algorithm Efficiency; Smaller Flop Count Is Not Always Better; Measuring Truncation Error; The Solution to Upper and Lower Triangular Systems; Efficiency Analysis; The Thomas Algorithm; Efficiency Analysis; Chapter Summary; Problems; MATLAB Problems; Conditioning of Problems and Stability of Algorithms; Why Do We Need Numerical Linear Algebra?; Computation Error; Forward Error; Backward Error; Algorithm Stability; Examples of Unstable Algorithms; Conditioning of a Problem
- Perturbation Analysis for Solving a Linear System
