A non-linear structure preserving matrix method for the low rank approximation of the Sylvester resultant matrix

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