### Friday, October 31

## MS11

Accurate Computation of Eigenproblems

10:00 AM-12:00 PM

*Room: Ballroom 1 *

We want to compute eigenvalues and invariant subspaces of Hermitian (and more generally: normal) matrices accurately. The ultimate goal is highly accurate and efficient numerical software. In the context of floating point computations we attain high accuracy by bounding relative rather than absolute eigenvalue errors, and by expressing invariant subspace bounds in terms of relative rather than absolute eigenvalue separations. Because of the close connection to Hermitian eigenvalue problems, we also discuss the computation of singular values and singular vector subspaces.

**Organizer: Ilse C. F. Ipsen**

*North Carolina State University*

**10:00 On the Eigenvalues of Indefinite Matrices**
*Kresimir Veselic*, Fernuniversitaet Hagen, Germany; Z. Drmac, University of Colorado, Boulder; and Striko E. Kovac, University of Zagreb, Croatia
**10:30 Relative Perturbation Bounds for Eigenvalues and Eigenvectors of Indefinite Hermitian Matrices**
*Ninoslav Truhar*, University Josip Juraj Strossmayer, Croatia; and Ivan Slapnicar, University of Split, Croatia
**11:00 Relative Error Bounds for Eigenvalues of Normal Matrices**
- Ilse C.F. Ipsen, Organizer
**11:30 More Accurate Bidiagonal Reduction for Computing the Singular Value Decomposition**
- Jesse L. Barlow, The Pennsylvania State University

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*MMD, 5/14/97*

*tjf, 6/13/97*

*MMD, 6/25/97*