Results 11 to 20 of about 4,353,527 (290)
On polynomial interpolation in the monomial basis [PDF]
SIAM Journal on Numerical Analysis, 2023 In this paper, we show that the monomial basis is generally as good as a well-conditioned polynomial basis for interpolation, provided that the condition number of the Vandermonde matrix is smaller than the reciprocal of machine epsilon.Comment: 26 pages,
Shen, Zewen, Serkh, Kirill
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Accurate Evaluation of Polynomials in Legendre Basis [PDF]
Journal of Applied Mathematics, 2014 This paper presents a compensated algorithm for accurate evaluation of a polynomial in Legendre basis. Since the coefficients of the evaluated polynomial are fractions, we propose to store these coefficients in two floating point numbers, such as double ...
Peibing Du, Hao Jiang, Lizhi Cheng
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A Dual Basis for Discrete Polynomial Blending
International Journal of Numerical Methods and Applications, 2016 “Discrete polynomial blending” is a term used to define a certain discretized version of curve blending whereby one approximates from the “sum of tensor product polynomial spaces” over sparse grids. We combine the theory of Boolean sum methods with dual
Kersey, Scott N.
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Structured matrix methods for computations on Bernstein basis polynomials [PDF]
, 2013 This thesis considers structure preserving matrix methods for computations on Bernstein polynomials whose coefficients are corrupted by noise. The ill-posed operations of greatest common divisor computations and polynomial division are considered, and it
Yang, Ning
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A gyroscopic polynomial basis in the sphere
Journal of Computational Physics, 2022 Standard spectral codes for full sphere dynamics utilize a combination of spherical harmonics and a suitableradial basis to represent fluid variables. These basis functions have a rotational invariance not present ingeophysical flows. Gyroscopic alignment - alignment of dynamics along the axis of rotation - is ahallmark of geophysical fluids in the ...
Abram C. Ellison +2 more
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Sparse multivariate polynomial interpolation on the basis of Schubert polynomials [PDF]
computational complexity, 2016 Schubert polynomials were discovered by A. Lascoux and M. Schützenberger in the study of cohomology rings of flag manifolds in 1980's. These polynomials generalize Schur polynomials, and form a linear basis of multivariate polynomials. In 2003, Lenart and Sottile introduced skew Schubert polynomials, which generalize skew Schur polynomials, and expand ...
Priyanka Mukhopadhyay, Youming Qiao
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Numerical Differentiation by the Polynomial-Exponential Basis
Journal of Applied and Industrial Mathematics, 2023 Our objective is to calculate the derivatives of data corrupted by noise. This is a challenging task as even small amounts of noise can result in significant errors in the computation. This is mainly due to the randomness of the noise, which can result in high-frequency fluctuations.
Phuong M. Nguyen +3 more
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Partial Differential Equations in Applied Mathematics, 2021 The localized method is one of the popular approaches in solving large-scale problems in science and engineering. In this paper, we implement the localized method of particular solutions using polynomial basis functions for solving various nonlinear ...
T. Dangal +2 more
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Polynomial degree reduction in the L2-norm on a symmetric interval for the canonical basis
Results in Applied Mathematics, 2021 In this paper, we develop a direct formula for determining the coefficients in the canonical basis of the best polynomial of degree M that approximates a polynomial of degree N>Mon a symmetric interval for the L2-norm.
Habib Ben Abdallah +2 more
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Canonical Basis and Macdonald Polynomials
Advances in Mathematics, 1998 In the basic representation of $U_q(\hat{sl}(2))$ realized via the algebra of symmetric functions we compare the canonical basis with the basis of Macdonald polynomials with $q=t^2$. We show that the Macdonald polynomials are invariant with respect to the bar involution defined abstractly on the representations of quantum groups. We also prove that the
Beck, Jonathan +2 more
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