Sparse Robust Rational Interpolation for Parameter-dependent Aerospace Models

Seshadri, Pranay; Constantine, Paul G.; Gonnet, Pedro; Parks, GT

doi:10.2514/6.2013-1680

Cited by 5 publications

(4 citation statements)

References 7 publications

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“…Our rational approximations are least-squares models, which can be formulated in a nonlinear or linearized fashion as we describe below. Our first approach is an extension of the algorithms for the linearized problem presented in [8,9,16]. The nonlinear problem is an example of a separable nonlinear least-squares problem, and algorithms for it often exploit this structure.…”

Section: Previous Work On Rational Approximationmentioning

confidence: 99%

“…We extend the method of these references to the multivariate case. One such extension has been proposed in [16]; our method may be viewed as a generalization of that extension to handle situations in which the data used to construct the model come from arbitrary sample points in the parameter space instead of from a tensor product grid.…”

Section: Multivariate Rational Models Via Linear Algebramentioning

confidence: 99%

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Multivariate Rational Approximation

Austin,

Krishnamoorthy,

Leyffer

et al. 2019

Preprint

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We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models for high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process to efficiently and robustly compute the coefficients of the rational approximation. Our second approach is based on an optimization formulation that allows us to include structural constraints on the rational approximation, resulting in a semi-infinite optimization problem that we solve using an outer approximation approach. We present results for synthetic and real-life HEP data, and we compare the approximation quality of our approaches with that of traditional polynomial approximations.

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Section: Previous Work On Rational Approximationmentioning

confidence: 99%

Section: Multivariate Rational Models Via Linear Algebramentioning

confidence: 99%

Multivariate Rational Approximation

Austin,

Krishnamoorthy,

Leyffer

et al. 2019

Preprint

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“…Unfortunately, rational approximation can be numerically fragile to compute, and it is inclined to spurious singularities. Many different approaches have been introduced to avoid these drawbacks, such as algorithms based on the singular value decomposition [28] or on a Stieltjes procedure and an optimization formulation [2].…”

mentioning

confidence: 99%

A linear barycentric rational interpolant on starlike domains

Berrut¹,

Elefante²

2022

etna

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When an approximant is accurate on an interval, it is only natural to try to extend it to multidimensional domains. In the present article we make use of the fact that linear rational barycentric interpolants converge rapidly toward analytic and several-times differentiable functions to interpolate them on two-dimensional starlike domains parametrized in polar coordinates. In the radial direction, we engage interpolants at conformally shifted Chebyshev nodes, which converge exponentially for analytic functions. In the circular direction, we deploy linear rational trigonometric barycentric interpolants, which converge similarly rapidly for periodic functions but now for conformally shifted equispaced nodes. We introduce a variant of a tensor-product interpolant of the above two schemes and prove that it converges exponentially for two-dimensional analytic functions-up to a logarithmic factor-and with an order limited only by the order of differentiability for real functions (provided that the boundary enjoys the same order of differentiability). Numerical examples confirm that the shifts permit one to reach a much higher accuracy with significantly fewer nodes, a property which is especially important in several dimensions.

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“…Unfortunately, rational approximation can be numerically fragile to compute and is inclined to spurious singularities. Many different approaches have been introduced to avoid these drawbacks, such as algorithms based on the singular value decomposition [32] or on a Stieltjes procedure and an optimization formulation [2].…”

mentioning

confidence: 99%

A linear barycentric rational interpolant on starlike domains

Berrut¹,

Elefante²

2021

Preprint

View full text Add to dashboard Cite

When an approximant is accurate on the interval, it is only natural to try to extend it to several-dimensional domains. In the present article, we make use of the fact that linear rational barycentric interpolants converge rapidly toward analytic and several times differentiable functions to interpolate on two-dimensional starlike domains parametrized in polar coordinates. In radial direction, we engage interpolants at conformally shifted Chebyshev nodes, which converge exponentially toward analytic functions. In circular direction, we deploy linear rational trigonometric barycentric interpolants, which converge similarly rapidly for periodic functions, but now for conformally shifted equispaced nodes. We introduce a variant of a tensor-product interpolant of the above two schemes and prove that it converges exponentially for two-dimensional analytic functions-up to a logarithmic factor-and with an order limited only by the order of differentiability for real functions, if the boundary is as smooth. Numerical examples confirm that the shifts permit to reach a much higher accuracy with significantly less nodes, a property which is especially important in several dimensions.

show abstract

Sparse Robust Rational Interpolation for Parameter-dependent Aerospace Models

Cited by 5 publications

References 7 publications

Multivariate Rational Approximation

Multivariate Rational Approximation

A linear barycentric rational interpolant on starlike domains

A linear barycentric rational interpolant on starlike domains

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