A parallel algorithm for discrete least squares rational approximation

Barel, Marc Van; Bultheel, Adhemar

doi:10.1007/bf01385850

Cited by 23 publications

(13 citation statements)

References 11 publications

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“…See also [5], In this context, it was observed only lately [9], [10], [2], [13], [3] We also assume that the number of data points m + 1 is at least equal to the number of unknowns 2n / 1 (recall that one coefficient is fixed by the monic normalization). x x x x x x x x x x x x X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X x x x x x x x x x x x x X X X X X X X X X X X X X X X X X X X X X X X X This case was considered in [15]. The missing link between the scalar and the block part is the initial condition for this block recurrence.…”

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Vector Orthogonal Polynomials and Least Squares Approximation

Bultheel¹,

Barel²

1995

SIAM J. Matrix Anal. & Appl.

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Abstract. We describe an algorithm for complex discrete least squares approximation, which turns out to be very efficient when function values are prescribed in points on the real axis or on the unit circle. In the case of polynomial approximation, this reduces to algorithms proposed by Rutishauser, Gragg, Harrod, Reichel, Ammar, and others. The underlying reason for efficiency is the existence of a recurrence relation for orthogonal polynomials, which are used to represent the solution. We show how these ideas can be generalized to least squares approximation problems of a more general nature.

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“…See also [7], [8]. Moreover it is well suited for implementation in a pipeline fashion on a parallel architecture [17], [15].…”

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Vector Orthogonal Polynomials and Least Squares Approximation

Bultheel¹,

Barel²

1995

SIAM J. Matrix Anal. & Appl.

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“…In both cases, the rational approximate can be obtained by a wide range of techniques [94,95,96,97]. In the hidden variable method, the rational approximation is reduced to a polynomial of second order by an identification process that is performed without approximation.…”

Section: Reduced Time-domain Models For the Environmentmentioning

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Dynamics of structures coupled with elastic media—A review of numerical models and methods

Clouteau

Cottereau

Lombaert

2013

Journal of Sound and Vibration

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This paper reviews issues and developments in the field of structure-environment interaction problems, in which the environment is an elastic body, possibly unbounded. It covers in particular the fields of soil-structure interaction, ground-borne noise and vibration emitted by transportation systems and wave diffraction by obstacles in an elastic medium. The general setting for a linear bounded structure coupled to an unbounded linear environment through a bounded interface is first recalled, and the domain decomposition technique classically used for its description is put up. Extensions for the cases of non-linear structure and uncertain environment are then discussed. Finally, the ongoing research in the fields of unbounded interface, moving interface, and multiple interfaces are reviewed and summarized.

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“…A generalization to unitary block-Hessenberg matrices and orthonormal polynomial vectors can be found in [27,28,10,29]. The size of the blocks of the matrix determines the degree structure of the sequence of corresponding orthonormal polynomial vectors.…”

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confidence: 99%

Unitary rank structured matrices

Delvaux

Barel

2008

Journal of Computational and Applied Mathematics

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In this paper we describe how one can represent a unitary rank structured matrix in an efficient way as a product of elementary unitary or Givens transformations. We also provide some basic operations for manipulating the representation, such as the transition to zero-creating form, the transition to a unitary/Givens-weight representation, as well as an internal pull-through process of the two branches of the representation. Finally, we characterize how to determine the 'shift' correction term to the rank structure, and we provide some applications to this result.

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A parallel algorithm for discrete least squares rational approximation

Cited by 23 publications

References 11 publications

Vector Orthogonal Polynomials and Least Squares Approximation

Vector Orthogonal Polynomials and Least Squares Approximation

Dynamics of structures coupled with elastic media—A review of numerical models and methods

Unitary rank structured matrices

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