Name
Abstract | ||
|---|---|---|
A square matrix can be reduced to simpler form via similarity transformations. Here "simpler form" may refer to diagonal (when possible), triangular (Schur), or Hessenberg form. Similar reductions exist for matrix pencils if we consider general equivalence transformations instead of similarity transformations. For both matrices and matrix pencils, well-established algorithms are available for each reduction, which are useful in various applications. For matrix polynomials, unimodular transformations can be used to achieve the reduced forms but we do not have a practical way to compute them. In this work we introduce a practical means to reduce a matrix polynomial with nonsingular leading coefficient to a simpler (diagonal, triangular, Hessenberg) form while preserving the degree and the eigenstructure. The key to our approach is to work with structure preserving similarity transformations applied to a linearization of the matrix polynomial instead of unimodular transformations applied directly to the matrix polynomial. As an application, we illustrate how to use these reduced forms to solve parameterized linear systems. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/17M1125182 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | Field | DocType |
triangularization,matrix polynomial,quasi-triangular,diagonalization,Hessen berg form,companion linearization,controller form linearization,equivalence,quadratic eigenvalue problem,Schur form,parameterized linear systems | Hessenberg matrix,Characteristic polynomial,Algebra,Polynomial matrix,Matrix (mathematics),Square matrix,Symmetric matrix,Band matrix,Mathematics,Block matrix | Journal |
Volume | Issue | ISSN |
39 | 1 | 0895-4798 |
Citations | PageRank | References |
0 | 0.34 | 4 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuji Nakatsukasa | 1 | 97 | 17.74 |
| Leo Taslaman | 2 | 3 | 1.48 |
| Françoise Tisseur | 3 | 455 | 58.80 |
| Ion Zaballa | 4 | 16 | 6.99 |