A Note on the Inversion of Sylvester Matrices in Control Systems | Zendy

Hongkui Li | Zendy; Ranran Li | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

A Note on the Inversion of Sylvester Matrices in Control Systems

Author(s) -

Hongkui Li,

Ranran Li

Publication year - 2011

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2011/609863

Subject(s) - sylvester's law of inertia , sylvester matrix , sylvester equation , invertible matrix , mathematics , inversion (geology) , matrix (chemical analysis) , pure mathematics , symmetric matrix , mathematical analysis , eigenvalues and eigenvectors , physics , paleontology , materials science , matrix polynomial , quantum mechanics , polynomial matrix , structural basin , polynomial , composite material , biology

We give a sufficient condition (the solvability of two standard equations) of Sylvester matrix by using the displacement structure of the Sylvester matrix, and, according to the sufficient condition, we derive a new fast algorithm for the inversion of a Sylvester matrix, which can be denoted as a sum of products of two triangular Toeplitz matrices. The stability of the inversion formula for a Sylvester matrix is also considered. The Sylvester matrix is numerically forward stable if it is nonsingular and well conditioned

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research