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From: przykry2004 <przykry2004@us...>  20040823 11:52:20

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 
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