Re: eigenvector computations
- To: mathgroup at smc.vnet.net
- Subject: [mg117360] Re: eigenvector computations
- From: "Hans Michel" <hmichel at cox.net>
- Date: Wed, 16 Mar 2011 06:26:52 -0500 (EST)
http://reference.wolfram.com/legacy/v5_2/Built-inFunctions/AdvancedDocumenta tion/LinearAlgebra/LinearAlgebraInMathematica/MatrixComputations/Eigensystem Computations/AdvancedDocumentationLinearAlgebra3.3.4.html Under Legacy >From Document Center in version 7 tutorial/LinearAlgebraMatrixComputations under Obsolete Scroll to "ARPACK". -----Original Message----- From: Bill Thurston [mailto:wpthurston at mac.com] Sent: Tuesday, March 15, 2011 6:05 AM To: mathgroup at smc.vnet.net Subject: [mg117360] [mg117328] eigenvector computations I'm doing some computations where I need to find the size of the leading eigenvalue of various matrices that depend on a rational number between 0 and 1. The matrices are mostly 0, with nonzero entries 1 or 2. I'm doing this using sparse matrices and, for a matrix A, asking for First@Abs[ Eigenvalues[ N[ A],1]] which usually works fine, but sometimes I get error messages like this: Eigenvalues::maxit2 : "Warning: maximum number of iterations, 1000, has been \ reached by the Arnoldi algorithm without convergence to the specified \ tolerance, but the current best computed value has been returned. You can use \ method options with Method -> {Arnoldi, opts} to increase the size of basis \ vectors, the maximum number of iterations, reduce the tolerance, or use an \ estimate as a shift, any of which may help." This would be fine except that I can't find any Mathematica documentation for the Arnoldi method or its options. What gives? Bill Thurston