Improved method for optimum choice of free parameter in orthogonal approximations

Tanguy, Noël; Morvan, R.; Vilbe, P.; Calvez, L.C.

doi:10.1109/78.782210

Cited by 14 publications

(6 citation statements)

References 11 publications

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“…This last technique has the great merit that the derivation of a solution requires knowledge of only few numerical characteristics of the signal under consideration. It has been generalized to a class of orthogonal functions, which satisfy a suitable differential or difference equation [15], [16], [17]. Unfortunately, the required differential or difference equation relative to continuous-and discrete-time Kautz functions haven't been established and the technique can't be used.…”

Section: Introductionmentioning

confidence: 99%

Pertinent choice of parameters for discrete Kautz approximation

Tanguy

Morvan²,

Vilbe³

et al. 2002

IEEE Trans. Automat. Contr.

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International audienceKautz functions have received much attention in the recent mathematical modeling and identification literature. These functions which involve free parameters can approximate efficiently signals with strong oscillatory behavior. We consider here the choice of the free parameters in discrete (two-parameter) Kautz approximation. Using a key relationship between Kautz and Laguerre expansions we derive an upper bound for the quadratic truncation error. Minimization of this upper bound yields pertinent parameters, whose computation then requires reduced knowledge of the function to be modeled

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Section: Introductionmentioning

confidence: 99%

Pertinent choice of parameters for discrete Kautz approximation

Tanguy

Morvan²,

Vilbe³

et al. 2002

IEEE Trans. Automat. Contr.

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“…To prove that, normalize GðsÞ as given in (7) by multiplying the denominator and the numerator by Z R ðsÞ, then substitute F k ðsÞ and Z k ðsÞ with their definition (5), (8) and reorganize the summation at the numerator, it follows (1 6 k 6 R) and consequently the R-first Müntz-Laguerre coefficients spectrum of FðsÞ and GðsÞ computed for a ¼ ½a 1 ; a 2 ; . .…”

Section: Appendix Amentioning

confidence: 99%

“…Given (5), (8) and the definition (2) it is straightforward to verify that functions E k ðsÞ (k ¼ 0; . .…”

Section: Model Definition and Identificationmentioning

confidence: 99%

“…They have a real multiple-order pole whose choice is of great importance for computing low-order and good quality models. Much work has been done on the subject and optimal methods [2][3][4][5] or sub-optimal methods [6][7][8] have been proposed in literature. However Laguerre functions are poorly suited to compact modeling of systems possessing several time constants or resonant characteristics.…”

Section: Introductionmentioning

confidence: 99%

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Parameter optimization of orthonormal basis functions for efficient rational approximations

Tanguy

Iassamen

Telescu

et al. 2015

Applied Mathematical Modelling

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International audienceIn this paper, the authors present an efficient procedure for optimal placement of poles in rational approximations by Müntz-Laguerre functions. The technique is formulated as the minimization of a quadratic criterion and the linear equations involved are efficiently expressed using the orthonormal basis functions. The presented technique has direct application in rational approximation and model order reduction of large-degree or infinite-dimensional systems. An efficient choice of parameters in orthogonal Müntz-Laguerre approximation Model order reduction of large-degree or infinite-dimensional systems The choice of Müntz-Laguerre parameters is based on a least squares optimization Abstract: In this paper, the authors present an efficient procedure for optimal placement of poles in rational approximations by Müntz-Laguerre functions. The technique is formulated as the minimization of a quadratic criterion and the linear equations involved are efficiently expressed using the orthonormal basis functions. The presented technique has direct application in rational approximation and model order reduction of large-degree or infinite-dimensional systems

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“…For our examples, we use the single-asset Black and Scholes framework. We study standard moving average options for different values of the averaging window δ as well as moving average options with delay (23).…”

Section: Numerical Examplesmentioning

confidence: 99%

A Finite-Dimensional Approximation for Pricing Moving Average Options

Bernhart¹,

Tankov²,

Warin³

2011

SIAM J. Finan. Math.

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We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average process based on a truncated Laguerre series expansion. The resulting problem is a finite-dimensional optimal stopping problem, which we propose to solve with a least squares Monte Carlo approach. We analyze the theoretical convergence rate of our method and present numerical results in the Black-Scholes framework.MSC 2010: 91G20, 33C45

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Improved method for optimum choice of free parameter in orthogonal approximations

Cited by 14 publications

References 11 publications

Pertinent choice of parameters for discrete Kautz approximation

Pertinent choice of parameters for discrete Kautz approximation

Parameter optimization of orthonormal basis functions for efficient rational approximations

A Finite-Dimensional Approximation for Pricing Moving Average Options

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