MatBackwardSolve#

Solves \(U x = b\), given a factored matrix, \(A = LU\). \(D^(1/2) U x = b\), given a factored symmetric matrix, \(A = U^T*D*U\),

Synopsis#

#include "petscmat.h" 
PetscErrorCode MatBackwardSolve(Mat mat, Vec b, Vec x)

Neighbor-wise Collective

Input Parameters#

mat - the factored matrix
b - the right-hand-side vector

Output Parameter#

x - the result vector

Notes#

MatSolve() should be used for most applications, as it performs a forward solve followed by a backward solve.

The vectors b and x cannot be the same. I.e., one cannot call MatBackwardSolve(A,x,x).

For matrix in MATSEQBAIJ format with block size larger than 1, the diagonal blocks are not implemented as \(D = D^(1/2) * D^(1/2)\) yet. MatForwardSolve() solves \(U^T*D y = b\), and MatBackwardSolve() solves \(U x = y\). Thus they do not provide a symmetric preconditioner.

Level#

developer

Location#

src/mat/interface/matrix.c

Implementations#

MatBackwardSolve_MKL_CPARDISO() in src/mat/impls/aij/mpi/mkl_cpardiso/mkl_cpardiso.c
MatBackwardSolve_MKL_PARDISO() in src/mat/impls/aij/seq/mkl_pardiso/mkl_pardiso.c

Index of all Mat routines
Table of Contents for all manual pages
Index of all manual pages