Look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems
نویسندگان
چکیده
منابع مشابه
A Block Toeplitz Look-ahead Schur Algorithm
This paper gives a look-ahead Schur algorithm for nding the symmetric factorization of a Hermitian block Toeplitz matrix. The method is based on matrix operations and does not require any relations with orthogonal polynomials. The simplicity of the matrix based approach ought to shed new light on other issues such as parallelism and numerical stability.
متن کاملA Block Toeplitz Look - Ahead Schur
This paper gives a look-ahead Schur algorithm for nding the symmetric factorization of a Hermitian block Toeplitz matrix. The method is based on matrix operations and does not require any relations with orthogonal polynomials. The simplicity of the matrix based approach ought to shed new light on other issues such as parallelism and numerical stability.
متن کاملSchur-type Algorithms for the Solution of Hermitian Toeplitz Systems via Factorization
In this paper fast algorithms for the solution of systems Tu = b with a strongly nonsingular hermitian Toeplitz coefficient matrix T via different kinds of factorizations of the matrix T are discussed. The first aim is to show that ZW-factorization of T is more efficient than the corresponding LU-factorization. The second aim is to design and compare different Schurtype algorithms for LUand ZW-...
متن کاملPreconditioners for Non-hermitian Toeplitz Systems 1
In this paper, we construct new !-circulant preconditioners for non-Hermitian Toeplitz systems, where we allow the generating function of the sequence of Toeplitz matrices to have zeros on the unit circle. We prove that the eigenvalues of the preconditioned normal equation are clustered at 1 and that for (N; N)-Toeplitz matrices with spectral condition number O(N) the corresponding PCG method r...
متن کاملLook-ahead Levinson- and Schur-type Recurrences in the Padé Table∗
For computing Padé approximants, we present presumably stable recursive algorithms that follow two adjacent rows of the Padé table and generalize the well-known classical Levinson and Schur recurrences to the case of a nonnormal Padé table. Singular blocks in the table are crossed by look-ahead steps. Ill-conditioned Padé approximants are skipped also. If the size of these lookahead steps is bo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 1995
ISSN: 0029-599X,0945-3245
DOI: 10.1007/s002110050116