Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Matrix Methods
- Part II Numerical Methods
- 6 Computational Linear Algebra
- 7 Numerical Methods for Differential Equations
- 8 Finite-Difference Methods for Boundary-Value Problems
- 9 Finite-Difference Methods for Initial-Value Problems
- Part III Least Squares and Optimization
- References
- Index
6 - Computational Linear Algebra
from Part II - Numerical Methods
Published online by Cambridge University Press: 18 February 2021
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Matrix Methods
- Part II Numerical Methods
- 6 Computational Linear Algebra
- 7 Numerical Methods for Differential Equations
- 8 Finite-Difference Methods for Boundary-Value Problems
- 9 Finite-Difference Methods for Initial-Value Problems
- Part III Least Squares and Optimization
- References
- Index
Summary
Computational linear algebra builds on the methods in Part I for solving systems of linear algebraic equations and the algebraic eigenproblem appropriate for small systems to methods amenable to approximate computer solutions for large systems.These include direct and iterative methods for solving systems of equations, such as LU decomposition and Gauss-Seidel iteration.A popular algorithm based on QR decomposition is described for solving large algebraic eigenproblems for the full spectrum of eigenpairs, and the Arnoldi method for a subset of eigenpairs of sparse matrices.
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- Publisher: Cambridge University PressPrint publication year: 2021