## LAPACK

### Summary

LAPACK is written in Fortran77 and provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided, as are related computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in both single and double precision.

### Authors

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### Status

incomplete information or not officially approved by the authors### Aims and scope

### Mathematical Classification

### Keywords

- backward error bounds
- banded matrices
- bidiagonal reduction
- Cholesky factorization
- column pivoting strategy
- Crawford's algorithm
- deflating subspaces
- dense matrices
- diagonal matrices
- eigenvalue problem
- eigenvalues
- eigenvectors
- equations solving
- forward error bounds
- generalized nonsymmetric eigenvalue problem
- generalized singular value decomposition
- Hager's method
- Hermitian eigenvalue problem
- Hessenberg reduction
- invariant subspaces
- linear algebra
- linear equality constrained least squares problems
- linear equation system solver
- linear least squares problems
- LQ factorization
- LU factorization
- matrices
- matrix
- matrix equilibration
- matrix factorization
- minimum norm solutions
- nonsymmetric eigenproblems
- orthogonal factorization
- orthogonal matrices
- permutation matrices
- positive definiteness
- QL factorization
- QR factorization
- RQ factorization
- Schur factorization
- Schur vectors
- simultaneous linear equation systems
- singular value decomposition
- singular value problems
- spectral factorization
- SVD factorization
- Sylvester equations
- symmetric eigenproblems
- trapezoidal matrices
- triangular matrices
- tridiagonal matrices
- underdetermined linear equation systems
- unitary matrices
- upper Hessenberg form
- upper triangular matrices
- vectorization