Program summary

Title of program: SUBROUTINE BOUNDS_OPT

Catalogue identifier: ADVE

Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland

Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVE

Computers: any computer that supports a Fortran 90 compiler

Operating systems: any computer that supports a Fortran 90 compiler

Programming language: Standard Fortran 90

High speed storage required: 5m+5 working-precision and 2m+7 integer for m Ritz values

No. of bits in a word: The floating point working precision is parameterized with the symbolic constant WP

No. of lines in distributed program, including test data, etc.: 2452

No. of bytes in distributed program, including test data, etc.: 281 543

Distribution format: tar.gz

Nature of physical problem: The computational solution of eigenvalue problems using iterative subspace methods has widespread applications in the physical sciences and engineering as well as other areas of mathematical modeling (economics, social sciences, etc.). The accuracy of the solution of such problems and the utility of those errors is a fundamental problem that is of importance in order to provide the modeler with information of the reliability of the computational results. Such applications include using these bounds to terminate the iterative procedure at specified accuracy limits.

Method of solution: The Ritz values and their residual norms are computed and used as input for the procedure. While knowledge of the exact eigenvalues is not required, we require that the Ritz values are isolated from the exact eigenvalues outside of the Ritz spectrum and that there are no skipped eigenvalues within the Ritz spectrum. Using a multipass refinement approach, upper and lower bounds are computed for each Ritz value.

Typical running time: While typical applications would deal with m<20, for , the running time is 0.12 s on an Apple PowerBook.