# Refining the Solution and Estimating Its Error

This section describes the LAPACK routines for refining the computed solution of a system of linear equations and estimating the solution error. You can call these routines after factorizing the matrix of the system of equations and computing the solution (see Routines for Matrix Factorization and Routines for Solving Systems of Linear Equations).

- ?gerfs
  Refines the solution of a system of linear equations with a general matrix and estimates its error.
- ?gbrfs
  Refines the solution of a system of linear equations with a general band matrix and estimates its error.
- ?gtrfs
  Refines the solution of a system of linear equations with a tridiagonal matrix and estimates its error.
- ?porfs
  Refines the solution of a system of linear equations with a symmetric (Hermitian) positive-definite matrix and estimates its error.
- ?pprfs
  Refines the solution of a system of linear equations with a packed symmetric (Hermitian) positive-definite matrix and estimates its error.
- ?pbrfs
  Refines the solution of a system of linear equations with a band symmetric (Hermitian) positive-definite matrix and estimates its error.
- ?ptrfs
  Refines the solution of a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal matrix and estimates its error.
- ?syrfs
  Refines the solution of a system of linear equations with a symmetric matrix and estimates its error.
- ?herfs
  Refines the solution of a system of linear equations with a complex Hermitian matrix and estimates its error.
- ?sprfs
  Refines the solution of a system of linear equations with a packed symmetric matrix and estimates the solution error.
- ?hprfs
  Refines the solution of a system of linear equations with a packed complex Hermitian matrix and estimates the solution error.
- ?trrfs
  Estimates the error in the solution of a system of linear equations with a triangular matrix.
- ?tprfs
  Estimates the error in the solution of a system of linear equations with a packed triangular matrix.
- ?tbrfs
  Estimates the error in the solution of a system of linear equations with a triangular band matrix.

Parent topic: Computational Routines