65Fxx Numerical linear algebra
This subtopic introduces the core ideas in numerical linear algebra, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Specific topics
65F05 Direct numerical methods for linear systems and matrix equations
Overview
Direct numerical methods for linear systems and matrix equations. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F08 Preconditioners for iterative methods
Overview
Preconditioners for iterative methods. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F10 Iterative numerical methods for linear systems
Overview
Iterative numerical methods for linear systems. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
Overview
Numerical computation of eigenvalues and eigenvectors of matrices. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F18 Numerical solution to inverse eigenvalue problems
Overview
Numerical solution to inverse eigenvalue problems. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F20 Numerical solutions to overdetermined systems, pseudoinverses
Overview
Numerical solutions to overdetermined systems, pseudoinverses. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F22 Ill-posedness and regularization of linear systems
Overview
Ill-posedness and regularization of linear systems. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F25 Orthogonalization in numerical linear algebra
Overview
Orthogonalization in numerical linear algebra. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F30 Other numerical algorithms for eigenvalue problems
Overview
Other numerical algorithms for eigenvalue problems. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F35 Numerical computation of matrix norms, conditioning, scaling
Overview
Numerical computation of matrix norms, conditioning, scaling. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F40 Numerical computation with sparse matrices
Overview
Numerical computation with sparse matrices. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F45 Null-space methods for linear systems
Overview
Null-space methods for linear systems. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F50 Sparse matrix algorithms
Overview
Sparse matrix algorithms. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F55 Parallel numerical methods for linear systems
Overview
Parallel numerical methods for linear systems. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks
65F60 Numerical computation of matrix functions
Overview
Numerical computation of matrix functions. This topic studies numerical linear algebra, including matrix factorizations, eigenproblems, and large-scale linear systems.
Related Wikipedia Page
Wikipedia: Numerical linear algebra
Useful Links
Key Ideas
- stable matrix factorizations
- iterative and direct solvers
- conditioning and backward error
Typical Uses
Used to solve large algebraic systems and spectral problems arising throughout scientific computing.
Applications
- Simulation and PDE discretizations
- Data science and dimensionality reduction
- Control and inverse problems
References
Recommended Textbooks