Update of /cvsroot/octave/octaveforge/main/sparse
In directory sc8prcvs1.sourceforge.net:/tmp/cvsserv22813
Modified Files:
pcg.m
Log Message:
Minor changes to the help text
Index: pcg.m
===================================================================
RCS file: /cvsroot/octave/octaveforge/main/sparse/pcg.m,v
retrieving revision 1.3
retrieving revision 1.4
diff u d r1.3 r1.4
 pcg.m 21 May 2004 14:26:31 0000 1.3
+++ pcg.m 23 Aug 2004 11:52:09 0000 1.4
@@ 24,12 +24,12 @@
%MAXIT, or PCG has less arguments, a default value equal to 20 is used.
%
%M is the (left) preconditioning matrix, so that the iteration is
%(theoretically) equivalent to solving by PCG P*x = M\B, with P = M\A or
%equivalently, P = inv(M)*A. Note that a proper choice of the preconditioner may
%dramatically improve the overall performance of the method! The user may pass
%for M a name of a function which returns the results of applying the inverse of
+%(theoretically) equivalent to solving by PCG P*x = M\B, with P = M\A.
+%Note that a proper choice of the preconditioner may
+%dramatically improve the overall performance of the method! Instead of matrix M,
+%the user may pass a function which returns the results of applying the inverse of
%M to a vector (usually this is the preferred way of using the preconditioner).
%If [] or eye(size(A)) is supplied for M, or M is omitted, no preconditioning is
+%If [] is supplied for M, or M is omitted, no preconditioning is
%applied.
%
%X0 is the initial guess. If X0 is empty or omitted, the function sets X0 to a
@@ 58,14 +58,16 @@
%Euclidean norm of the residual, and RESVEC(i,2) is the preconditioned residual
%norm, after the (i1)th iteration, i = 1,2,...ITER+1. The preconditioned
%residual norm is defined as r^2 = r'*(M\r) where r = BA*x, see also the
%description of M. If EIGEST is not required, only RELRES(:,1) is returned.
+%description of M. If EIGEST is not required, only RESVEC(:,1) is returned.
%
%EIGEST returns the estimate for the smallest (EIGEST(1)) and largest
%(EIGEST(2)) eigenvalues of the preconditioned matrix P (see the description of
%M for the definition of P). In particular, if no preconditioning is used, the
+%(EIGEST(2)) eigenvalues of the preconditioned matrix P=M\A.
+%In particular, if no preconditioning is used, the
%estimates for the extreme eigenvalues of A are returned. EIGEST(1) is an
%overestimate and EIGEST(2) is an underestimate, so that EIGEST(2)/EIGEST(1) is
%a lower bound for cond(P,2). The method works only for symmetric positive
+%a lower bound for cond(P,2), which nevertheless in the limit should
+%theoretically be equal to the actual value of the condition number.
+%The method which computes EIGEST works only for symmetric positive
%definite A and M, and the user is responsible for verifying this assumption.
%
%EXAMPLES
