Barycentric Lagrange Interpolation

By Jean-Paul Berrut, Lloyd N. Trefethen. 2004

1,279 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Mechanics of Materials, Numerical Analysis, Evaluation & Benchmarks

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Citations in the corpus

A Tight and Unified Analysis of Extragradient for a Whole Spectrum of Differentiable Games (2019, methodology): “Hence, using the barycentric formula, λ k | sign( L k ( λ k +1 )) at the points λ 1 , . . . | | | However, from Berrut and Trefethen (2004, Section 3), , λ j evaluated at λ k +1 . and by Berrut and Trefethen (2004, Eq.”
Fast, numerically stable computation of oscillatory integrals with stationary points (2010, methodology): “We use the barycentric formula [3] for intermediate values of x.”
Resolving the conflict between generality and plausibility in verified computation (2013, methodology): “We can use Barycentric Lagrange interpolation [14] to write:”
Clustering-based short-term load forecasting for residential electricity under the increasing-block pricing tariffs in China (2018, methodology): “The collected dataset contains some missing values, considering that the number of data samples is not very large, this study uses the Lagrange interpolation [5] to fill in the missing values.”
Linearization of matrix polynomials expressed in polynomial bases (2008, neutral): “[7, 15]).”
Experimental and numerical investigation of inertial particle clustering in isotropic turbulence (2008, methodology): “Fluid velocities at particle centres are obtained via an eighth-order Lagrangian interpolation scheme similar to that described in Berrut & Trefethen (2004).”
A simple embedding method for solving partial differential equations on surfaces (2008, methodology): “One may carry out the polynomial interpolation dimensionby-dimension using one-dimensional barycentric Lagrange interpolation [2].”
Rectangular spectral collocation (2015, methodology): “The barycentric interpolation formula (Berrut & Trefethen, 2004) is an ideal tool for this task.”
Barycentric rational interpolation with no poles and high rates of approximation (2007, methodology): “The polynomial interpolant pn itself can be expressed in barycentric form by letting w i = n ∏ j=0,j 6=i 1 x i −x j , (2) a fact first observed by Taylor [22] and Dupuy [10], and the favourable numerical aspects of this way of evaluating Lagrange interpolants are summarized by Berrut and Trefethen [”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, positive): “A computationally more efficient and reliable form is obtained if one uses the barycentric form of Lagrange interpolation [52].”
PaCAL: A Python Package for Arithmetic Computations with Random Variables (2014, methodology): “Finally, we need to mention the Chebfun package (Battels and Trefethen 2004; Trefethen and others 2011) which uses the same methodology to implement computations on arbitrary functions, and was the main inspiration for us.”
A spectral element approach for the stability of delay systems (2011, methodology): “The barycentric formula requires less computational effort and has better numerical stability than the conventional Lagrange representation [52, 55]; therefore, it was used to generate the trial functions in the present study.”
Arithmetic Operations on Independent Random Variables: A Numerical Approach (2012, methodology): “It turns out that such an approximation can very easily be achieved using the so-called barycentric interpolation formula [2]”
A family of A-stable Runge–Kutta collocation methods of higher order for initial-value problems (2007, methodology): “They have been widely used in numerical analysis (Reddy & Weideman, 2005; Berrut & Trefethen, 2004; Panowsky & Richardson, 1988; Vigo-Aguiar & Ramos, 2003).”