## [Octave-cvsupdate] octave-forge/main/sparse pcg.m,1.3,1.4

 [Octave-cvsupdate] octave-forge/main/sparse pcg.m,1.3,1.4 From: przykry2004 - 2004-08-23 11:52:20 ```Update of /cvsroot/octave/octave-forge/main/sparse In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv22813 Modified Files: pcg.m Log Message: Minor changes to the help text Index: pcg.m =================================================================== RCS file: /cvsroot/octave/octave-forge/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 (i-1)-th iteration, i = 1,2,...ITER+1. The preconditioned %residual norm is defined as |||r|||^2 = r'*(M\r) where r = B-A*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 ```

 [Octave-cvsupdate] octave-forge/main/sparse pcg.m,1.3,1.4 From: przykry2004 - 2004-08-23 11:52:20 ```Update of /cvsroot/octave/octave-forge/main/sparse In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv22813 Modified Files: pcg.m Log Message: Minor changes to the help text Index: pcg.m =================================================================== RCS file: /cvsroot/octave/octave-forge/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 (i-1)-th iteration, i = 1,2,...ITER+1. The preconditioned %residual norm is defined as |||r|||^2 = r'*(M\r) where r = B-A*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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