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# 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.


## See Also
 [](ch_matrices), `Mat`, `MatForwardSolve()`, `MatGetFactor()`, `MatSolve()`, `MatForwardSolve()`

## Level
developer

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/interface/matrix.c.html#MatBackwardSolve">src/mat/interface/matrix.c</A>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/mat/interface/matrix.c)


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