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
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