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Patents: Publications:
  • T.Bella, Y.Eidelman, I.Gohberg, V.Olshevsky, Computations with quasiseparable matrices and polynomials , to appear in Theoretical Computer Science, 2008.
  • T.Bella, V.Olshevsky and P.Zhlobich, Classifications of recurrence relations via subclasses of (H,m)-quasiseparable matrices, submitted.
  • T.Bella, V.Olshevsky and P.Zhlobich, Signal Flow Graphs Approach to Inversion of (H,m)-Quasiseparable Vandermonde Matrices and New Filter Structures , submitted.
  • T.Bella, V.Olshevsky and U.Prasad, Lipschitz stability of canonical Jordan bases of H-selfadjoint matrices under structure-preserving perturbations, Linear Algebra and its Applications, Volume 428, Issues 8-9, 15 April 2008, Pages 2130-2176.
  • T.Bella, V.Olshevsky, L. Sakhnovich, Ranks of Hadamard Matrices and Equivalence of Sylvester Hadamard and Pseudo-Noise Matrice, In Recent Advances in Matrix and Operator Theory, Operator Theory: Advances and Applications, Volume 179, Birkhдuser Basel, 2008.
  • T.Bella, Y.Eidelman, I.Gohberg, V.Olshevsky, E.Tyrtyshnikov, P.Zhlobich, A Traub-like algorithm for Hessenberg-quasiseparable-Vandermonde matrices of arbitrary order , accepted, February 2008.
  • T.Bella, Y.Eidelman, I.Gohberg, V.Olshevsky, Computations with quasiseparable polynomials and matrices , submitted, January 2008.
  • T.Bella, V.Olshevsky, P.Zhlobich, Characterization of (H,m) quasiseparable matrices and their subclasses via recurrence relations and signal flow graphs, February, 2008.
  • T.Bella, Y.Eidelman, I.Gohberg, V.Olshevsky, Characterization of (H,1) quasiseparable matrices and their subclasses via recurrence relations and signal flow graphs, preprint.
  • T.Bella, Y.Eidelman, I.Gohberg, V.Olshevsky, E.Tyrtyshnikov, Fast inversion of Hessenberg-quasiseparable-Vandermonde matrices and resulting recurrence relations and characterizations, preprint.
  • T.Bella, Y.Eidelman, I.Gohberg, I.Koltracht, V.Olshevsky, A Bjorck-Pereyra-type algorithm for solving Quasiseparable-Vandermonde systems, preprint.
  • V.Olshevsky, I. Oseledets, E.Tyrtyshnikov Superfast inversion of two-level Toeplitz matrices using Newton iteration and tensor-displacement structure, to appear in "Recent Advances in Matrix and Operator Theory," Birkhauser Verlag.
  • T.Bella, Y.Eidelman, I.Gohberg, I.Koltracht, V.Olshevsky, A Bjorck-Pereyra-type algorithm for Szego-Vandermonde matrices based on properties of unitary Hessenberg matrices, Linear Algebra and Applications, Volume 420, Issues 2-3 pp. 634-647 (2007)
  • T. Bella, V. Olshevsky, L. Sakhnovich, Equivalence of Hadamard matrices and pseudo-noise matrices , In Advanced Signal Processing Algorithms, Architectures, and Implementations XV. Editor(s): Franklin T. Luk, SPIE Publications, Aug 2005, p. 265-271.
  • Vadim Olshevsky, L Sakhnovich, A generalized Kharitonov theorem for quasi-polynomials and entire functions occurring in systems with multiple and distributed delays In Advanced Signal Processing Algorithms, Architectures, and Implementations XV. Editor(s): Franklin T. Luk, SPIE Publications, Aug 2005, p. 325-336.
  • V.Olshevsky and L.Sakhnovich, Matched filters for generalized stationary processes, IEEE Transactions on Information Theory 51(9): 3308-3313 (2005).
  • Yu.Eidelman, I.Gohberg and V.Olshevsky, The QR iteration method for Hermitian quasiseparable matrices of an arbitrary order, Linear Algebra and its Applications, Volume 404, 15 July 2005, Pages 305-324
  • V.Olshevsky, I.Oseledets and E.Tyrtyshnikov, Tensor properties of multilevel Toeplitz and related matrices, Linear Algebra and its Applications, Volume 412, Issue 1, 1 January 2006, Pages 1-21
  • Yu.Eidelman, I.Gohberg and V.Olshevsky, Eigenstructure of Order-One-Quasiseparable Matrices. Three-term and Two-term Recurrence Relations, Linear Algebra and its Applications, Volume 405, 1 August 2005, Pages 1-40
  • V.Olshevsky and L.Sakhnovich, Prediction for generalized stationary processes, In Recent Advances in Operator Theory and Its Applications The Israel Gohberg Anniversary Volume Series: Operator Theory: Advances and Applications, Vol. 160 Kaashoek, Marinus A.; Seatzu, Sebastiano; Mee, Cornelis van der (Eds.) 2005, p. 257-266.
  • A.Olshevsky and V.Olshevsky, Kharitonov's theorem and Hermite's criterion, Linear Algebra and its Applications, Volume 399, 1 April 2005, Pages 285-297
  • T.Kailath and V.Olshevsky. Displacement structure approach to discrete trigonometric transform based preconditioners of G.Strang and T.Chan types. SIAM Journal on Matrix Analysis and Applications Volume 26, Number 3 pp. 706-734, 2005.
  • Alexander Olshevsky, Vadim Olshevsky, Jun Wang. A comrade-matrix-based derivation of the different versions of fast cosine and sine transforms. Proc. SPIE Vol. 5205, Dec. 2003, p. 399-410, Advanced Signal Processing Algorithms, Architectures, and Implementations XIII; Franklin T. Luk; Ed.
  • V. Olshevsky, Pivoting for structured matrices and rational tangential interpolation, in Fast Algorithms for Structured Matrices: Theory and Applications, CONM/323, p. 1 - 75, AMS publications, May 2003.
  • V. Olshevsky and M. A. Shokrollahi, A displacement approach to decoding algebraic codes, in Fast Algorithms for Structured Matrices: Theory and Applications, CONM/323, p. 265 - 292, AMS publications, May 2003.
  • A. Olshevsky, V. Olshevsky, and J. Wang, A comrade-matrix-based derivation of the eight versions of fast cosine and sine transforms, in Fast Algorithms for Structured Matrices: Theory and Applications, CONM/323, p. 119-150, AMS publications, May 2003.
  • T.Boros, T.Kailath and V.Olshevsky, Pivoting and Backward Stability of Fast Algorithms for Solving Cauchy Linear Equations, Linear Algebra and Its Applications, Vol 343/344, March 2002.
  • V.Olshevsky and Michael Stewart. Stable Factorization of Hankel and Hankel-like Matrices. Numerical Linear Algebra, Vol 8, Issue 6/7, p 401-434, 2001. (Special Issue: Numerical Linear Algebra Techniques for Control and Signal Processing.) .
  • G.Heinig, V.Olshevsky, The Schur algorithm for matrices with Hessenberg displacement structure, in ``Structured Matrices in Mathematics, Computer Science, and Engineering II,'' Contemporary Mathematics series, Vol 281, 3-16, AMS, 2001.
  • V.Olshevsky and Amin Shokrollahi, A Superfast Algorithm for Confluent Rational Tangential Interpolation Problem via Matrix-vector Multiplication for Confluent Cauchy-like Matrices, in ``Structured Matrices in Mathematics, Computer Science, and Engineering I,'' Contemporary Mathematics series, Vol 280, 32-46, AMS, 2001.
  • Dario Fasino and V.Olshevsky. How bad are symmetric Pick matrices. in ``Structured Matrices in Mathematics, Computer Science, and Engineering I,'' Contemporary Mathematics series, Vol 280, 301-312, AMS, 2001.
  • V.Olshevsky, Unitary Hessenberg matrices and the generalized Parker-Forney-Traub algorithm for inversion of Szego-Vandermonde matrices. invited chapter in the book ``Structured Matrices: Recent Developments in Theory and Computation,'' 67-78, (D.Bini, E. Tyrtyshnikov, P. Yalamov., Eds.), 2001, NOVA Science Publ., USA.
  • V.Olshevsky and A.Shokrollahi, Fast matrix-vector multiplication algorithms for confluent Cauchy-like matrices with applications, in Proc of of the Thirty Second ACM Symposium on Theory of Computing (STOC'00), p.573-581; ACM, New York, 2000.
  • V.Olshevsky and A.Shokrollahi. A displacement structure approach to efficient decoding of Reed-Solomon and algebraic geometric codes. A conference paper appeared in Proc of of the Thirty First ACM Symposium on Theory of Computing. (STOC'99), p.235-244; ACM, New York, 1999.
  • T.Boros, T.Kailath and V.Olshevsky, Fast Bjorck-Pereyra-type algorithm for parallel solution of Cauchy linear equations, Linear Algebra and Its Applications, 302-303 (1999), p.265-293.
  • V.Olshevsky and V.Pan, Polynomial and rational evaluation and interpolation (with structured matrices), Automata, languages and programming (Prague, 1999), 585--594, Lecture Notes in Comput. Sci., 1644, Springer, Berlin, 1999.
  • V.Olshevsky and M.Stewart, Stable factorization of Hankel and Hankel-like matrices, in Advanced Signal Processing Algorithms, Architectures, and Implementations, SPIE publications, 1999, 334-349.
  • V.Olshevsky and A.Shokrollahi, A Unified Superfast Algorithm for Confluent Tangential interpolation problems, in Advanced Signal Processing Algorithms, Architectures, and Implementations, SPIE publications, 1999, 312-323.
  • V.Olshevsky and Victor Pan, A unified superfast algorithm for boundary rational tangential interpolation problems and for inversion and factorization of dense strauctured matrices. Proc. of 39th Annual Symposium on Foundations of Computer Science (FOCS'98), IEEE Computer Society, Los Alamitos, CA, 1998, 192-201.
  • V.Olshevsky. Eigenvector computation for almost unitary Hessenberg matrices and inversion of Szego-Vandermonde matrices via Discrete Transmission lines. Linear Algebra and Its Applications, 285 (1998), 37-67.
  • T. Kailath, and V. Olshevsky. Displacement structure approach to polynomial Vandermonde and related matrices. Linear Algebra and Appl, 261(1997), 49-90.
  • Kailath and V.Olshevsky. Diagonal Pivoting for Partially Reconstructible Cauchy-like Matrices, With Applications to Toeplitz-like Linear Equations and to Boundary Rational Matrix Interpolation Problems. Linear Algebra and Appl, 254 (1997), 251-302.
  • I.Gohberg and V.Olshevsky. The fast generalized Parker-Traub algorithm for inversion of Vandermonde and related matrices. J. of Complexity, 13(2) (1997), 208-234.
  • V.Matsaev and V.Olshevsky. Cyclic dimensions, kernel multiplicities and Gohberg-Kaashoek numbers. Linear Algebra Appl., 239 (1996), 161-174 .
  • T.Kailath and V.Olshevsky. Displacement structure approach to discrete trigonometric transform based preconditioners of G.Strang and T.Chan types. Calcolo, (33) 1996, 191-208.
  • Gohberg and V.Olshevsky, Fast inversion of Vandermonde and Vandermonde-like matrices, pp. 205-221, in Communications, Computation, Control and Signal Processing: A tribute to Thomas Kailath, Eds. A.Paulraj, V Roychowdhury and C.Shaper, Kluwer Academic Publishing, 1996.
  • I.Gohberg, T.Kailath and V. Olshevsky. Fast Gaussian elimination with partial pivoting for matrices with displacement structure. Math. of Computation,   64 No. 212 (1995), 1557-1576.
  • T.Kailath and V. Olshevsky. Displacement structure approach to Chebyshev-Vandermonde and related matrices. Integral Equations and Operator Theory,   22 (1995), 65-92.
  • I.Gohberg and V. Olshevsky. Fast state space algorithms for matrix Nehari and Nehari-Takagi interpolation problems. Integral Equations and Operator Theory,   20 (1994), 44-83. A conference paper appeared in Proc. of MTNS-93, Systems and Networks: Mathematical Theory and Applications, v.2, Invited and Contributed Papers, edited by U. Helmke, R. Mennicken and J. Sauers, Academy Verlag,1994, p. 687-690.
  • I.Gohberg and V. Olshevsky. Fast algorithms with preprocessing for matrix-vector multiplication problems. Journal of Complexity,   10 (1994), 411-427.
  • I.Gohberg and V. Olshevsky. Fast inversion of Chebyshev-Vandermonde matrices. Numerische Mathematik,   67 (1994), 71-92.
  • I.Gohberg and V. Olshevsky. Complexity of multiplication with vectors for structured matrices. Linear Algebra Appl.,   202 (1994), 163-192.
  • A.Markus and V. Olshevsky. Complete controllability and assignment of the spectrum in infinite dimensional spaces. Integral Equations and Operator Theory,   17 (1993), 107-122.
  • I.Gohberg and V. Olshevsky. Circulants, displacements and decompositions of matrices. Integral Equations and Operator Theory,   15 (1992), 730-743.
  • V. Olshevsky. Similarity of block diagonal and block triangular matrices. Integral Equations and Operator Theory,   15 (1992), 853-863.
  • V. Olshevsky. Change of Jordan structure of G-selfadjoint operators and selfadjoint operator functions under small perturbations, (in Russian), Izvestia Akad. nauk U.S.S.R.,   54 (No. 5) (1990), 1021 - 1048. English translation : AMS, Math. U.S.S.R. Izvestia, 37 (No. 2) (1991), 371 - 396.
  • V. Olshevsky. A condition for the closeness of the sets of invariant subspaces of the close matrices in terms of their Jordan structures, (in Russian), Siberian Math. Journal,   30 (No. 4) (1989), 102 - 110. English translation : Siberian Math. Journal, Plenum publishing corp., 30 (No. 4) (1989), 580 - 586.
  • A.Markus and V. Olshevsky. Exact controllability and spectrum assignment in infinite dimensional spaces, (in Russian), Matematicheskie Issledovania,   108 (1989), 97 -114.
  • V. Olshevsky. On distance between invariant subspaces of operators in finite dimensional spaces, (in Russian), Izvestia Akad. nauk M.S.S.R.,   1 (1989), 65-66.
  • V. Olshevsky. Variation of the Jordan structure of G-selfadjoint operators and selfadjoint operator-functions under small perturbations, (in Russian), Functional Analysis and its Applications,   22 (No. 3) (1988), 79-80; English translation : Functional Analysis and its Applications, Plenum publishing corp., 22 (No. 3) (1988), 236 - 237.
  • V. Olshevsky. Semi-stability of dimension of linear span of eigenvectors and generalized eigenvectors of holomorphic operator-function, (in Russian), Matematicheskie Issledovania,   93 (1988), 119-128.
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Structured matrices displacement structure Toeplitz Hankel Vandermonde Bezoutian Cauchy Pick Loewner semiseparable quasiseparable OR iteration Nevanlinna Schur Levinson Hadamard Gohberg Krein fast algorithm FFT DFT DCT DST orthogonal polynomials Szego error analysis LU factorization rational matrix interpolation Kharitonov theorem filtering estimation coding theory stability complexity preconditioner unitary Hessenberg transmission lines структурные матрицы структурированные Матрица Адамара Ганкеля Гильберта Теплица Вандермонда Уилкинсона Безутианты Пика Коши Левнера семисепарабельная квазисепарабельная неванлинна Шур Левинсон Адамар Быстрые алгоритмы быстрое препбразование фурье ортогональные многочлены Сеге рациональная матричная интерполяция теорема Харитонова фильтрация теория кодирования коды устойчивость предобуславливатель многоуровневые унитарные хессенберга