Title of Paper:Lagrange-type basis for multivariate uniform integrable tensor-product Birkhoff interpolation

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Date of Publication:2017-12-01

Journal:MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Included Journals:SCIE

Volume:40

Issue:18

Page Number:6823-6831

ISSN No.:0170-4214

Key Words:multivariate Birkhoff interpolation; uniform; integrable; tensor-product type; Lagrange-type basis

Abstract:Birkhoff interpolation is the most general interpolation scheme. We study the Lagrange-type basis for uniform integrable tensor-product Birkhoff interpolation. We prove that the Lagrange-type basis of multivariate uniform tensor-product Birkhoff interpolation can be obtained by multiplying corresponding univariate Lagrange-type basis when the integrable condition is satisfied. This leads to less computational complexity, which drops to O(N-1(3) + N-2(3) center dot center dot center dot + N-n(3)) from O(N-1(3) N-2(3) center dot center dot center dot N-n(3)).