Name
Abstract | ||
|---|---|---|
Let A = (aij) be an n × n Toeplitz matrix with bandwidth k + 1, k = r + s, that is, aij = aj−i, i, j = 1,… ,n, ai = 0 if i > s and if i < -r. We compute p(λ)= det(A - λI), as well as p(λ)/p′(λ), where p′(λ) is the first derivative of p(λ), by using O(k log k log n) arithmetic operations. Moreover, if ai are m × m matrices, so that A is a banded Toeplitz block matrix, then we compute p(λ), as well as p(λ)p′(λ), by using O(m3k(log2 k + log n) + m2k log k log n) arithmetic operations. The algorithms can be extended to the computation of det(A − λB) and of its first derivative, where both A and B are banded Toeplitz matrices. The algorithms may be used as a basis for iterative solution of the eigenvalue problem for the matrix A and of the generalized eigenvalue problem for A and B. |
Year | DOI | Venue |
|---|---|---|
1991 | 10.1016/0885-064X(91)90028-V | Journal of Complexity |
DocType | Volume | Issue |
Journal | 7 | 4 |
ISSN | Citations | PageRank |
0885-064X | 2 | 0.54 |
References | Authors | |
6 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dario Bini | 1 | 590 | 108.78 |
| Victor Pan | 2 | 62 | 9.52 |