petsc-3.7.1 2016-05-15
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# PCCP

a "column-projection" preconditioner This is a terrible preconditioner and is not recommended, ever! Many br

Loops over the entries of x computing dx_i to Many br

           min || b - A(x + dx_i e_i ||_2

           dx_i

       That is, it changes a single entry of x to minimize the new residual.

      Let A_i represent the ith column of A, then the minimization can be written as

          min || r - (dx_i) A e_i ||_2

          dx_i

      or   min || r - (dx_i) A_i ||_2

           dx_i

       take the derivative with respect to dx_i to obtain

           dx_i = (A_i^T A_i)^(-1) A_i^T r

       This algorithm can be thought of as Gauss-Seidel on the normal equations

Notes: This proceedure can also be done with block columns or any groups of columns Many brbut this is not coded. Many br

These "projections" can be done simultaneously for all columns (similar to Jacobi) Many bror sequentially (similar to Gauss-Seidel/SOR). This is only coded for SOR type. Many br

This is related to, but not the same as "row projection" methods. Many br

This is currently coded only for SeqAIJ matrices in sequential (SOR) form. Many br

Many br

### See Also

PCCreate(), PCSetType(), PCType (for list of available types), PCJACOBI, PCSOR

Level:intermediate
Location:src/ksp/pc/impls/cp/cp.c
Index of all PC routines
Table of Contents for all manual pages
Index of all manual pages