schur_iter
Schur iterative.
Syntax
[a, aa, L, U] = schur_iter(a, b, L, U, A12, A21, A22, tol, maxit, varargin)
Description
Performs Schur decomposition by an iterative method and solves the
augmented system [A11, A12; A21, A22]x = [b1; b2], where A11 = LU,
A11 mxm, A12 mxn, A21 nxm and A22 nxn, b = [b1, b2]' (nxm)x1. To
factorize A11 do [L, U] = lu(A11). The Schur complement is not
explicitly computed.
Input (required)
a = previous solution of the problem.
b = rhs of the system.
L = lower triangular factor from LU factorization of A.
U = upper triangular factor from LU factorization of A.
A12 = right-upper block for augmented matrix.
A21 = left-lower block for augmented matrix.
A22 = right-lower block for augmented matrix.
tol = tolerance.
maxit = max. nb. iterations allowed.
Input (optional)
precond = use precond or not ('no', 'ilu', 'diag').
for 'ndiad' define: 'numbd' (number of diagonals);
for 'ilu' define: 'milu', 'typeilu', 'droptol',
'thresh' and 'udiag'.
Output
a = next solution of the augmented problem.
aa = coefficients of the error estimation.
L = augmented matrix lower triangular factor.
U = augmented matrix upper triangular factor.
See also
schur_luinc, schur_luinc2 and schur_nflu.
Performs Schur decomposition by an iterative method and solves the augmented system [A11, A12; A21, A22]x = [b1; b2], where A11 = LU, A11 mxm, A12 mxn, A21 nxm and A22 nxn, b = [b1, b2]' (nxm)x1. To factorize A11 do [L, U] = lu(A11). The Schur complement is not explicitly computed.
Input (required)
a = previous solution of the problem.
b = rhs of the system.
L = lower triangular factor from LU factorization of A.
U = upper triangular factor from LU factorization of A.
A12 = right-upper block for augmented matrix.
A21 = left-lower block for augmented matrix.
A22 = right-lower block for augmented matrix.
tol = tolerance.
maxit = max. nb. iterations allowed.
Input (optional)
precond = use precond or not ('no', 'ilu', 'diag').
for 'ndiad' define: 'numbd' (number of diagonals);
for 'ilu' define: 'milu', 'typeilu', 'droptol',
'thresh' and 'udiag'.
Output
a = next solution of the augmented problem.
aa = coefficients of the error estimation.
L = augmented matrix lower triangular factor.
U = augmented matrix upper triangular factor.
See also
schur_luinc, schur_luinc2 and schur_nflu.
precond = use precond or not ('no', 'ilu', 'diag'). for 'ndiad' define: 'numbd' (number of diagonals); for 'ilu' define: 'milu', 'typeilu', 'droptol', 'thresh' and 'udiag'.
Output
a = next solution of the augmented problem.
aa = coefficients of the error estimation.
L = augmented matrix lower triangular factor.
U = augmented matrix upper triangular factor.
See also
schur_luinc, schur_luinc2 and schur_nflu.
schur_luinc, schur_luinc2 and schur_nflu.