By Richard B. Lehoucq, Danny C. Sorensen, C. Yang

A advisor to knowing and utilizing the software program package deal ARPACK to resolve huge algebraic eigenvalue difficulties. The software program defined relies at the implicitly restarted Arnoldi approach. The e-book explains the purchase, install, services, and targeted use of the software program.

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Extra info for ARPACK Users' Guide: Solution of Large-scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods

Example text

Corresponding to each distinct eigenvalue A e

The remainder of this section discusses additional transformations that may be applied to convert a generalized eigenproblem to a standard eigenproblem. These are appropriate when M is well conditioned (Hermitian or non-Hermitian). 1) to provides a transformation to a standard eigenvalue problem. In this case, a request for a matrix-vector product would be satisfied with the following three steps: 1. Solve LHz — v for z; 2. Matrix-vector multiply z *— Az; 3. Solve Lw = z for w. Upon convergence, a computed eigenvector y for (L^ALr^) is converted to an eigenvector x of the original problem by solving the triangular system L^x = y.

B) DP = A and B = I. 2. Shift-invert mode (iparam(7) = 3, bmat = ' I ' ) . Use driver zndrv2. (a) Solve Ax = xA in shift-invert mode. (b) OP = (A - crl)-1 and B = I. 3. Regular inverse mode (iparam(7) = 2, bmat = } G ' ) . Use driver zndrvS. (a) Solve Ax = MxA in regular inverse mode. (b) OP = M~ X A and B = M. 4. Shift-invert mode (iparam(7) = 3, bmat = J G ' ) . Use driver zndrv4. (a) Solve Ax — MxA in shift-invert mode. (b) OP = (A - ffMJ-'M and B = M. 40 General Use of ARPACK c c c c c c c c c c c I % I No fatal errors occurred.

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