Vadim Olshevsky - Academia.edu (original) (raw)

Vadim Olshevsky

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Papers by Vadim Olshevsky

Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)

In this paper we propose a general scheme to study Bezoutians that is based on the method known a... more In this paper we propose a general scheme to study Bezoutians that is based on the method known as the method of operator identities in the operator theory literature [S76b, S97, S99] (its finite dimensional counterpart is known under the name displacement structure method in the engineering [KKM79, K99] and in matrix theory and numerical literature [HR84, O03]). The latter approach allows us to introduce a generalized concept of the operator Bezoutian and to carry over to it the classical results of Jacobi (on common roots of scalar polynomials [J1836]), and of Hermite (on polynomial stability [H1856]). Several other known results scattered in the mathematical and engineering literature (Krein [K] Krein [K], Sakhnovich [S76a], Gohberg-Heinig [GH76], Anderon-Jury [AJ76], Lerer-Tysmenetsky [LT82], Lerer-Rodman [LR96a, LR96b]) are shown to appear as particular instances of our general scheme. The unified operator identities (displacement structure) approach results in a transparent co...

Linear Algebra and its Applications, 2006

Linear Algebra and its Applications, 2005

Proceedings of the thirty-first annual ACM symposium on Theory of Computing, 1999

Advanced Signal Processing Algorithms, Architectures, and Implementations XV, 2005

Advanced Signal Processing Algorithms, Architectures, and Implementations IX, 1999

The classical Caratheodory-Fejer and Nevanlinna-Pick interpolation problems have a long and disti... more The classical Caratheodory-Fejer and Nevanlinna-Pick interpolation problems have a long and distinguished history, appearing in a variety of applications in mathematics and electrical engineering. It is well-known that these problems can be solved in O(n2) operations, where n is the overall multiplicity of interpolation points. In this paper we suggest a superfast algorithm for solving the more general confluent tangential interpolation problem. The cost of the new algorithm varies from O(n log2 n) to O(n log3 n), depending on the multiplicity pattern of the interpolation points. The new algorithm can be used to factorize, invert, and solve a linear system of equations with confluent- Cauchy-like matrices. This class of matrices includes Hankel-like (i.e., permuted Toeplitz-like), Vandermonde-like and Cauchy-like matrices as special cases. An important ingredient of the proposed method is a new fast algorithm to compute a product of a confluent- Cauchy-like matrix by a vector.