New fast algorithms for polynomial interpolation and evaluation on the Chebyshev node set
نویسندگان
چکیده
منابع مشابه
Multivariate polynomial interpolation on Lissajous-Chebyshev nodes
In this contribution, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets linked to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation nodes related to these curves, we derive a discrete orthogonality structure on these node sets. Using this discrete orthogonality structure, we can deriv...
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Stable polynomial evaluation and interpolation at n Chebyshev or adjusted (expanded) Chebyshev points is performed using O(nlog’ n) arithmetic operations, to be compared with customary algorithms either using on the order of n* operations or being unstable. We also evaluate a polynomial of degree d at the sets of n Chebyshev or adjusted (expanded) Chebyshev points using O(dlog d log n) if n 5 d...
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We study the problem of reconstructing a sparse polynomial in a basis of Chebyshev polynomials (Chebyshev basis in short) from given samples on a Chebyshev grid of [−1, 1]. A polynomial is called M -sparse in a Chebyshev basis, if it can be represented by a linear combination of M Chebyshev polynomials. For a polynomial with known and unknown Chebyshev sparsity, respectively, we present efficie...
متن کاملPolynomial Evaluation and Interpolation: Fast and Stable Approximate Solution
Multipoint polynomial evaluation and interpolation are fundamental for modern algebraic and numerical computing. The known algorithms solve both problems over any field by using O(N log N) arithmetic operations for the input of size N , but the cost grows to quadratic for numerical solution. Our study results in numerically stable algorithms that use O(uN log N) arithmetic time for approximate ...
متن کاملAlgorithms for Accurate, Validated and Fast Polynomial Evaluation
Algorithms for Accurate, Validated and Fast Polynomial Evaluation∗ Stef Graillat†, Philippe Langlois‡ and Nicolas Louvet§ †PEQUAN, LIP6, Université Pierre et Marie Curie, CNRS, Paris, France E-mail: [email protected] ‡DALI, ELIAUS, Université de Perpignan Via Domitia, France E-mail: [email protected] §Arénaire, LIP, INRIA, Université de Lyon, CNRS, France E-mail: [email protected]
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1998
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(97)00283-6