petsc-3.6.4 2016-04-12
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Implements Paul Fischer's initial guess algorithm Method 1 and 2 for situations where a linear system is solved repeatedly


PetscErrorCode  KSPFischerGuessCreate(KSP ksp,PetscInt method,PetscInt maxl,KSPFischerGuess *itg)


Notes: the algorithm is different from the paper because we do not CHANGE the right hand side of the new problem and solve the problem with an initial guess of zero, rather we solve the original new problem with a nonzero initial guess (this is done so that the linear solver convergence tests are based on the original RHS.) But we use the xtilde = x - xguess as the new direction so that it is not mostly orthogonal to the previous solutions.

These are not intended to be used directly, they are called by KSP automatically when the KSP option KSPSetFischerGuess(KSP,PetscInt,PetscInt) or -ksp_guess_fischer <int,int>

Method 2 is only for positive definite matrices, since it uses the A norm.

This is not currently programmed as a PETSc class because there are only two methods; if more methods are introduced it should be changed. For example the Knoll guess should be included

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