The arnoldi process, short recursions, and displacement ranks

✍ Scribed by Hongyuan Zha; Zhenyue Zhang

• Book ID: 104156333
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 878 KB
• Volume: 249
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(97)82725-5

✦ Synopsis

We introduce two new methods for generating an orthonormal basis of a Krylov subspace spanned by the columns of K,( A, r) = (r, Ar, . . . , A"-'r) with A an arbitrary matrix. We show that both of the methods produce short recursions when AeH = p(A), h w ere p(h) is a polynomial of low degree. This property of A also leads to the low-displacement-rank structure of the cross-product matrix

&,(A, rjHK,(A, r). 0 Elseuier Science Inc., 1996