Refining the Solution and Estimating Its Error: LAPACK Computational Routines

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 coefficient matrix and estimates its error.
• ?gerfsx
  Uses extra precise iterative refinement to improve the solution to the system of linear equations with a general coefficient matrix A and provides error bounds and backward error estimates.
• ?gbrfs
  Refines the solution of a system of linear equations with a general band coefficient matrix and estimates its error.
• ?gbrfsx
  Uses extra precise iterative refinement to improve the solution to the system of linear equations with a banded coefficient matrix A and provides error bounds and backward error estimates.
• ?gtrfs
  Refines the solution of a system of linear equations with a tridiagonal coefficient matrix and estimates its error.
• ?porfs
  Refines the solution of a system of linear equations with a symmetric (Hermitian) positive-definite coefficient matrix and estimates its error.
• ?porfsx
  Uses extra precise iterative refinement to improve the solution to the system of linear equations with a symmetric/Hermitian positive-definite coefficient matrix A and provides error bounds and backward error estimates.
• ?pprfs
  Refines the solution of a system of linear equations with a symmetric (Hermitian) positive-definite coefficient matrix stored in a packed format and estimates its error.
• ?pbrfs
  Refines the solution of a system of linear equations with a band symmetric (Hermitian) positive-definite coefficient matrix and estimates its error.
• ?ptrfs
  Refines the solution of a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal coefficient matrix and estimates its error.
• ?syrfs
  Refines the solution of a system of linear equations with a symmetric coefficient matrix and estimates its error.
• ?syrfsx
  Uses extra precise iterative refinement to improve the solution to the system of linear equations with a symmetric indefinite coefficient matrix A and provides error bounds and backward error estimates.
• ?herfs
  Refines the solution of a system of linear equations with a complex Hermitian coefficient matrix and estimates its error.
• ?herfsx
  Uses extra precise iterative refinement to improve the solution to the system of linear equations with a symmetric indefinite coefficient matrix A and provides error bounds and backward error estimates.
• ?sprfs
  Refines the solution of a system of linear equations with a packed symmetric coefficient matrix and estimates the solution error.
• ?hprfs
  Refines the solution of a system of linear equations with a packed complex Hermitian coefficient matrix and estimates the solution error.
• ?trrfs
  Estimates the error in the solution of a system of linear equations with a triangular coefficient matrix.
• ?tprfs
  Estimates the error in the solution of a system of linear equations with a packed triangular coefficient matrix.
• ?tbrfs
  Estimates the error in the solution of a system of linear equations with a triangular band coefficient matrix.