论文信息 - A Sharp Version of Kahan ' s Theorem on Clustered Eigenvalues

A Sharp Version of Kahan ' s Theorem on Clustered Eigenvalues

Let n n Hermitian matrix A have eigenvalues 1; 2; ; n, and let k k Hermitian matrix H have eigenvalues 1 2 k, and let Q be an n k matrix having full column rank, so 1 k n. It is proved that there exist k eigenvalues i1 i2 ik of A such that max 1 j k j j ij j c min(Q) kAQ QHk2; This material is based in part upon the third author's work supported by Argonne National Laboratory under grant No. 20552402 and the University of Tennessee through the Advanced Research Projects Agency under contract No. DAAL03-91-C-0047, by the National Science Foundation under grant No. ASC-9005933, and by the National Science Infrastructure grants No. CDA-8722788 and CDA-9401156. Supported by the State Major Key Project for Basic Researches of China. Supported by the State Major Key Project for Basic Researches of China.

Z. Cao | Zhi-hao Cao

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