CONJUGATE
GRADIENT ALGORITHM
*
* To solve Ax = b given the preconditioning matrix C inverse and
* an initial approximation x(0):
*
* INPUT: the number of equations and unknowns n; the entries
* A(I,J), 1<=I, J<=n, of the matrix A; the entries
* B(I), 1<=I<=n, of the inhomogeneous term b; the
* entries C(I,J), 1<=I, J<=n, of the matrix C inverse,
* the entries XO(I), 1<=I<=n, of x(0); tolerance TOL;
* maximum number of iterations N.
*
* OUTPUT: the approximate solution X(1),...,X(n) or a message
* that the number of iterations was exceeded.
GAUSS-SEIDEL
ITERATAIVE TECHNIQUE ALGORITHM
*
* To solve Ax = b given an initial approximation x(0).
*
* INPUT: the number of equations and unknowns n; the entries
* A(I,J), 1<=I, J<=n, of the matrix A; the entries
* B(I), 1<=I<=n, of the inhomogeneous term b; the
* entries XO(I), 1<=I<=n, of x(0); tolerance TOL;
* maximum number of iterations N.
*
* OUTPUT: the approximate solution X(1),...,X(n) or a message
* that the number of iterations was exceeded.
ITERATIVE
REFINEMENT ALGORITHM
*
* To approximate the solution to the linear system Ax=b when A is
* suspected to be ill-conditioned:
*
* INPUT: The number of equations and unknowns n; the entries
* A(i,j), 1<=i, j<=n, of the matrix A; the entries b(i),
* 1<=i<=n, of the inhomogeneous term b; the maximum number
* of iterations N.
*
* OUTPUT: The approximation XX(1),...,XX(n) or a message that the
* number of iterations was exceeded.
JACOBI ITERATIVE
ALGORITHM
* To solve Ax = b given an initial approximation x(0).
*
* INPUT: the number of equations and unknowns n; the entries
* A(I,J), 1<=I, J<=n, of the matrix A; the entries
* B(I), 1<=I<=n, of the inhomogeneous term b; the
* entries XO(I), 1<=I<=n, of x(0); tolerance TOL;
* maximum number of iterations N.
*
* OUTPUT: the approximate solution X(1),...,X(n) or a message
* that the number of iterations was exceeded.
SOR ALGORITHM
*
* To solve Ax = b given the parameter w and an initial approximation
* x(0):
*
* INPUT: the number of equations and unknowns n; the entries
* A(I,J), 1<=I, J<=n, of the matrix A; the entries
* B(I), 1<=I<=n, of the inhomogeneous term b; the
* entries XO(I), 1<=I<=n, of x(0); tolerance TOL;
* maximum number of iterations N; parameter w (omega).
*
* OUTPUT: the approximate solution X(1),...,X(n) or a message
* that the number of iterations was exceeded.