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A Traub–like algorithm for HessenbergquasiseparableVandermonde
"... matrices of arbitrary order T.Bella ∗ , Y.Eidelman † , I.Gohberg † , V.Olshevsky ∗ , E.Tyrtyshnikov ‡ and P.Zhlobich ∗ Abstract. Although Gaussian elimination uses O(n 3) operations to invert an arbitrary matrix, matrices with a special Vandermonde structure can be inverted in only O(n 2) operations ..."
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special cases, e.g., monomials, real orthogonal polynomials and the Szegö polynomials, as well as new subclasses. We derive a fast O(n 2) Traub–like algorithm to invert the associated (H, m)–quasiseparable–Vandermonde matrices. The class of quasiseparable matrices is garnering a lot of attention recently
Applying QuasiSeparability to Markovian Process Algebra
 University of Verona
, 1998
"... Stochastic process algebras have become an accepted part of performance modelling over recent years. Because of the advantages of compositionality and flexibility they are increasingly being used to model larger and more complex systems. Therefore tools which support the evaluation of models express ..."
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Cited by 11 (5 self)
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Stochastic process algebras have become an accepted part of performance modelling over recent years. Because of the advantages of compositionality and flexibility they are increasingly being used to model larger and more complex systems. Therefore tools which support the evaluation of models expressed using stochastic process algebra must be able to utilise the full range of decomposition and solution techniques available. In this paper we study a class of models which do not give rise to a product form solution but can nevertheless be decomposed into their components without loss of generality. We also exemplify the use of the Markovian process algebra PEPA with the spectral expansion technique which enables a class of PEPA models with infinite state space to be solved numerically. 1 Introduction The advantages of using a stochastic process algebra to specify performance models are well documented (see Hillston [9] for example). In brief, a process algebra allows models to be compare...
Signal Flow Graph Approach to Inversion of (H, m)–quasiseparable Vandermonde Matrices and New Filter Structures
"... Abstract. We use the language of signal flow graph representation of digital filter structures to solve three purely mathematical problems, including fast inversion of certain polynomial–Vandermonde matrices, deriving an analogue of the Horner and Clenshaw rules for polynomial evaluation in a (H, m) ..."
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Abstract. We use the language of signal flow graph representation of digital filter structures to solve three purely mathematical problems, including fast inversion of certain polynomial–Vandermonde matrices, deriving an analogue of the Horner and Clenshaw rules for polynomial evaluation in a (H, m)–quasiseparable
Eigenstructure of OrderOneQuasiseparable Matrices. Threeterm and Twoterm Recurrence Relations, Linear Algebra and its Applications, Volume 405
, 2005
"... This paper presents explicit formulas and algorithms to compute the eigenvalues and eigenvectors of orderonequasiseparable matrices. Various recursive relations for characteristic polynomials of their principal submatrices are derived. The cost of evaluating the characteristic polynomial of an N × ..."
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Cited by 10 (4 self)
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This paper presents explicit formulas and algorithms to compute the eigenvalues and eigenvectors of orderonequasiseparable matrices. Various recursive relations for characteristic polynomials of their principal submatrices are derived. The cost of evaluating the characteristic polynomial of an N
Gegenbauer polynomials and semiseparable matrices
, 2007
"... Abstract. In this paper, we develop a new algorithm for converting coefficients between expansions in different families of Gegenbauer polynomials up to a finite degree. To this end, we show that the corresponding linear mapping is represented by the eigenvector matrix of an explicitly known diagona ..."
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Cited by 3 (1 self)
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be applied to an arbitrary vector at cost. All algorithms are accurate up to a prefixed accuracy. We provide brief numerical results. Key words. Gegenbauer polynomials, polynomial transforms, semiseparable matrices, eigendecomposition, spectral divideandconquer methods AMS subject classifications. 42C10
Fast Approximation Algorithms for Computations with Cauchy Matrices, Polynomials and Rational Functions
 Proc. of the Ninth International Computer Science Symposium in Russia (CSR’2014
"... The papers [MRT05], [CGS07], [XXG12], and [XXCB14] combine the techniques of the Fast Multipole Method of [GR87], [CGR98] with the transformations of matrix structures, traced back to [P90]. The resulting numerically stable algorithms approximate the solutions of Toeplitz, Hankel, Toeplitzlike, and ..."
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Cited by 3 (3 self)
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with a large class of matrices that have structure of Cauchy or Vandermonde type and for the evaluation and interpolation of polynomials and rational functions. We detail and analyze the new algorithms, and in [Pa] we extend them further.
Fast Approximation Algorithms for Cauchy Matrices, Polynomials and Rational Functions?
"... Abstract. The papers [MRT05], [CGS07], [XXG12], and [XXCBa] have combined the advanced FMM techniques with transformations of matrix structures (traced back to [P90]) in order to devise numerically stable algorithms that approximate the solutions of Toeplitz, Hankel, Toeplitzlike, and Hankellike l ..."
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Cited by 1 (1 self)
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like linear systems of equations in nearly linear arithmetic time, versus classical cubic time and quadratic time of the previous advanced algorithms. We show that the power of these approximation algorithms can be extended to yield similar results for computations with other matrices that have displacement
Results 1  10
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204