# Routines for Solving Systems of Linear Equations

This section describes the LAPACK routines for solving systems of linear equations. Before calling most of these routines, you need to factorize the matrix of your system of equations (see Routines for Matrix Factorization). However, the factorization is not necessary if your system of equations has a triangular matrix.

- ?getrs
  Solves a system of linear equations with an LU-factored square matrix, with multiple right-hand sides.
- ?gbtrs
  Solves a system of linear equations with an LU-factored band matrix, with multiple right-hand sides.
- ?gttrs
  Solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by ?gttrf.
- ?potrs
  Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite matrix.
- ?pptrs
  Solves a system of linear equations with a packed Cholesky-factored symmetric (Hermitian) positive-definite matrix.
- ?pbtrs
  Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite band matrix.
- ?pttrs
  Solves a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal matrix using the factorization computed by ?pttrf.
- ?sytrs
  Solves a system of linear equations with a UDU- or LDL-factored symmetric matrix.
- ?hetrs
  Solves a system of linear equations with a UDU- or LDL-factored Hermitian matrix.
- ?sptrs
  Solves a system of linear equations with a UDU- or LDL-factored symmetric matrix using packed storage.
- ?hptrs
  Solves a system of linear equations with a UDU- or LDL-factored Hermitian matrix using packed storage.
- ?trtrs
  Solves a system of linear equations with a triangular matrix, with multiple right-hand sides.
- ?tptrs
  Solves a system of linear equations with a packed triangular matrix, with multiple right-hand sides.
- ?tbtrs
  Solves a system of linear equations with a band triangular matrix, with multiple right-hand sides.

Parent topic: Computational Routines