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Existence of ℋ-matrix approximants to the inverse FE-matrix of elliptic operators withL∞-coefficients

✍ Scribed by Mario Bebendorf; Wolfgang Hackbusch

Book ID
105878635
Publisher
Springer-Verlag
Year
2003
Tongue
English
Weight
471 KB
Volume
95
Category
Article
ISSN
0029-599X

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Existence of a low rank or ℋ-matrix appr
Existence of a low rank or ℋ-matrix approximant to the solution of a Sylvester equation
✍ L. Grasedyck 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 190 KB

## Abstract We consider the Sylvester equation __AX__−__XB__+__C__=0 where the matrix __C__∈ℂ^__n__×__m__^ is of low rank and the spectra of __A__∈ℂ^__n__×__n__^ and __B__∈ℂ^__m__×__m__^ are separated by a line. We prove that the singular values of the solution X decay exponentially, that means for