Name
Title | ||
|---|---|---|
Vector Spaces of Linearizations for Matrix Polynomials: A Bivariate Polynomial Approach. |
Abstract | ||
|---|---|---|
We revisit the landmark paper [D. S. Mackey et al. SIAM J. Matrix Anal. Appl., 28 (2006), pp. 971-1004] and, by viewing matrices as Coefficients for bivariate polynomials, we provide concise proofs for key properties of linearizations for matrix polynomials. We also show that every pencil in the double ansatz space is intrinsically connected to a Bezout matrix, which we use to prove the eigenvalue exclusion theorem. In addition our exposition allows for any polynomial basis and for any field. The new viewpoint also leads to new results. We generalize the double ansatz space by exploiting its algebraic interpretation as a space of Bezout pencils to derive new linearizations with potential applications in the theory of structured matrix polynomials. Moreover, we analyze the conditioning of double ansatz space linearizations in the important practical case of a Chebyshev basis. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1137/15M1013286 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | Field | DocType |
matrix polynomials,bivariate polynomials,Bezoutian,double ansatz space,degree-graded polynomial basis,orthogonal polynomials,conditioning | Polynomial basis,Ansatz,Polynomial matrix,Orthogonal polynomials,Polynomial,Algebra,Mathematical analysis,Matrix (mathematics),Bézout matrix,Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
38 | 1 | 0895-4798 |
Citations | PageRank | References |
5 | 0.45 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuji Nakatsukasa | 1 | 97 | 17.74 |
| Vanni Noferini | 2 | 26 | 6.83 |
| Alex Townsend | 3 | 113 | 15.69 |