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Your search keyword '"Olshevsky, Vadim"' showing total 179 results
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179 results on '"Olshevsky, Vadim"'

1. Gohberg-Kaashoek Numbers and Forward Stability of the Schur Canonical Form

Author

Minenkova, Anastasiia, Nitch-Griffin, Evelyn, and Olshevsky, Vadim

Subjects
Mathematics - Classical Analysis and ODEs, Mathematics - Numerical Analysis, 65F99
Abstract

In the present paper we complete the stability of Schur decomposition depending on the Jordan structure of the perturbation, started in \cite{MNO}., Comment: 18 pages. arXiv admin note: text overlap with arXiv:2108.02312

Published
2021

2. Backward Stability of the Schur Canonical Form

Author

Minenkova, Anastasiia, Nitch-Griffin, Evelyn, and Olshevsky, Vadim

Subjects
Mathematics - Classical Analysis and ODEs, Mathematics - Numerical Analysis, 65F99
Abstract

In the present paper, we show the backward stability of the Schur decomposition for a given matrix under small perturbation., Comment: 19 pages

Published
2021

3. Existence of flipped orthogonal conjugate symmetric Jordan canonical bases for real H-selfadjoint matrices.

Author

Dogruer Akgul, Sahinde, Minenkova, Anastasiia, and Olshevsky, Vadim

Abstract

For real matrices selfadjoint in an indefinite inner product there are two special canonical Jordan forms, that is (i) flipped orthogonal (FO) and (ii) γ-conjugate symmetric (CS). These are the classical Jordan forms with certain additional properties induced by the fact that they are H-selfadjoint. In this paper, we prove that for any real H-selfadjoint matrix, there is a γ-FOCS Jordan form that is simultaneously flipped orthogonal and γ-conjugate symmetric. [ABSTRACT FROM AUTHOR]

Published
2024
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4. A Fast Algorithm for the Inversion of Quasiseparable Vandermonde-like Matrices

Author

Perera, Sirani M., Bonik, Grigory, and Olshevsky, Vadim

Subjects
Mathematics - Numerical Analysis, Computer Science - Symbolic Computation, 15A09, 15B05, 65Y04
Abstract

The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast Gaussian elimination algorithm for the polynomial Vandermonde-like matrices. Later we use the said algorithm to derive fast inversion algorithms for quasiseparable, semiseparable and well-free Vandermonde-like matrices having $\mathcal{O}(n^2)$ complexity. To do so we identify structures of displacement operators in terms of generators and the recurrence relations(2-term and 3-term) between the columns of the basis transformation matrices for quasiseparable, semiseparable and well-free polynomials. Finally we present an $\mathcal{O}(n^2)$ algorithm to compute the inversion of quasiseparable Vandermonde-like matrices.

Published
2014

8. Introduction

Author

Lerer, Leonid, Olshevsky, Vadim, Spitkovsky, Ilya, Gohberg, Israel, editor, Ball, Joseph A., editor, Dym, Harry, editor, Kaashoek, Marinus A., editor, Langer, Heinz, editor, Tretter, Christiane, editor, Adamyan, Vadim, editor, Böttcher, Albrecht, editor, Brown, B. Malcolm, editor, Curto, Raul, editor, Gesztesy, Fritz, editor, Kurasov, Pavel, editor, Lerer, Leonid E., editor, Paulsen, Vern, editor, Putinar, Mihai, editor, Rodman, Leiba, editor, Spitkovsky, Ilya M., editor, Lerer, Leonid, editor, and Olshevsky, Vadim, editor

Published
2010
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9. Ranks of Hadamard Matrices and Equivalence of Sylvester—Hadamard and Pseudo-Noise Matrices

Author

Bella, Tom, Olshevsky, Vadim, Sakhnovich, Lev, Gohberg, I., editor, Alpay, D., editor, Arazy, J., editor, Atzmon, A., editor, Ball, J. A., editor, Ben-Artzi, A., editor, Bercovici, H., editor, Böttcher, A., editor, Clancey, K., editor, Coburn, L. A., editor, Curto, R. E., editor, Davidson, K. R., editor, Douglas, R. G., editor, Dijksma, A., editor, Dym, H., editor, Fuhrmann, P. A., editor, Gramsch, B., editor, Helton, J. A., editor, Kaashoek, M. A., editor, Kaper, H. G., editor, Kuroda, S. T., editor, Lancaster, P., editor, Lerer, L. E., editor, Mityagin, B., editor, Olshevsky, V., editor, Putinar, M., editor, Rodman, L., editor, Rovnyak, J., editor, Sarason, D. E., editor, Spitkovsky, I. M., editor, Treil, S., editor, Upmeier, H., editor, Verduyn Lunel, S. M., editor, Voiculescu, D., editor, Xia, D., editor, Yafaev, D., editor, Ball, Joseph A., editor, Eidelman, Yuli, editor, Helton, J. William, editor, Olshevsky, Vadim, editor, and Rovnyak, James, editor

Published
2008
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10. Superfast Inversion of Two-Level Toeplitz Matrices Using Newton Iteration and Tensor-Displacement Structure

Author

Olshevsky, Vadim, Oseledets, Ivan, Tyrtyshnikov, Eugene, Gohberg, I., editor, Alpay, D., editor, Arazy, J., editor, Atzmon, A., editor, Ball, J. A., editor, Ben-Artzi, A., editor, Bercovici, H., editor, Böttcher, A., editor, Clancey, K., editor, Coburn, L. A., editor, Curto, R. E., editor, Davidson, K. R., editor, Douglas, R. G., editor, Dijksma, A., editor, Dym, H., editor, Fuhrmann, P. A., editor, Gramsch, B., editor, Helton, J. A., editor, Kaashoek, M. A., editor, Kaper, H. G., editor, Kuroda, S. T., editor, Lancaster, P., editor, Lerer, L. E., editor, Mityagin, B., editor, Olshevsky, V., editor, Putinar, M., editor, Rodman, L., editor, Rovnyak, J., editor, Sarason, D. E., editor, Spitkovsky, I. M., editor, Treil, S., editor, Upmeier, H., editor, Verduyn Lunel, S. M., editor, Voiculescu, D., editor, Xia, D., editor, Yafaev, D., editor, Ball, Joseph A., editor, Eidelman, Yuli, editor, Helton, J. William, editor, Olshevsky, Vadim, editor, and Rovnyak, James, editor

Published
2008
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12. Optimal Prediction of Generalized Stationary Processes

Author

Olshevsky, Vadim, Sakhnovich, Lev, Gohberg, Israel, editor, Alpay, D., editor, Arazy, J., editor, Atzmon, A., editor, Ball, J. A., editor, Ben-Artzi, A., editor, Bercovici, H., editor, Böttcher, A., editor, Clancey, K., editor, Coburn, L. A., editor, Davidson, K. R., editor, Douglas, R. G., editor, Dijksma, A., editor, Dym, H., editor, Fuhrmann, P. A., editor, Gramsch, B., editor, Heinig, G., editor, Helton, J. A., editor, Kaashoek, M. A., editor, Kaper, H. G., editor, Kuroda, S. T., editor, Lancaster, P., editor, Lerer, L. E., editor, Mityagin, B., editor, Peller, V. V., editor, Rodman, L., editor, Rovnyak, J., editor, Sarason, D. E., editor, Spitkovsky, I. M., editor, Treil, S., editor, Upmeier, H., editor, Verduyn Lunel, S. M., editor, Voiculescu, D., editor, Widom, H., editor, Xia, D., editor, Yafaev, D., editor, Kaashoek, Marinus A., editor, Seatzu, Sebastiano, editor, and van der Mee, Cornelis, editor

Published
2005
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16. Matched filtering for generalized stationary processes

Author

Olshevsky, Vadim and Sakhnovich, Lev

Subjects
Electric filters -- Research, Information theory -- Research
Abstract

The methods for solving optimal filtering problems in the case of the classical stationary processes have been well known since the late 1940s. Practice often gives rise to what is not a classical stationary process but a generalized one, and white noise is one simple example. Hence, it is of interest to describe the system action on the generalized stationary processes, and then to carry over filtering methods to them. For arbitrary generalized stochastic processes this seems to be a challenging problem. In this correspondence, we identify a rather general class of [S.sub.J]-generalized stationary processes for which the desired extension can be done for matched filters. This class can be considered as a model of colored noise, and it is wide enough to include white noise, positive frequencies white noise, as well as certain generalized processes occurring in practice, namely, when the smoothing effect gives rise to the situation in which the distribution of probabilities may not exist at some time instances. One advantage of the suggested model is that it connects optimal filter design with inverting of integral operators; the methods for the latter can be found in the extensive literature. Index Terms--Generalized stationary processes, Gohberg-Semencul formula, integral equations, matched filters, positive-frequencies white noise.

Published
2005

27. A Fast Algorithm for the Inversion of Quasiseparable Vandermonde-like Matrices

Author

2411947, Perera, Sirani M., Bonik, Grigory, Olshevsky, Vadim, 2411947, Perera, Sirani M., Bonik, Grigory, and Olshevsky, Vadim

Abstract

The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast Gaussian elimination algorithm for the polynomial Vandermonde-like matrices. Later we use the said algorithm to derive fast inversion algorithms for quasiseparable, semiseparable and well-free Vandermonde-like matrices having O(n2) complexity. To do so we identify structures of displacement operators in terms of generators and the recurrence relations(2-term and 3-term) between the columns of the basis transformation matrices for quasiseparable, semiseparable and well-free polynomials. Finally we present an O(n2) algorithm to compute the inversion of quasiseparable Vandermonde-like matrices.

Published
2014

37. Stable factorization of Hankel and Hankel-like matrices

Author

Olshevsky, Vadim, Stewart, Michael, Olshevsky, Vadim, and Stewart, Michael

Abstract

This paper gives displacement structure algorithms for the factorization positive defjnite and indefinite Hankel and Hankel-like matrices. The positive definite algorithm uses orthogonal symplectic transformations in place of the E-orthogonal transformations used in Toeplitz algorithms. The indefinite algorithm uses a look-ahead step and is based on the observation that displacement structure algorithms for Hankel factorization have a natural and simple block generalization. Both algorithms can be applied to Hankel-like matrices of arbitrary displacement rank.

Published
1998

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