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Lagrange‐type basis for multivariate uniform integrable tensor‐product Birkhoff interpolation
Author(s) -
Xu Lili,
Lei Na
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4495
Subject(s) - mathematics , tensor product , birkhoff interpolation , interpolation (computer graphics) , integrable system , lagrange polynomial , univariate , type (biology) , basis (linear algebra) , mathematical analysis , trigonometric interpolation , product (mathematics) , multivariate statistics , trilinear interpolation , polynomial interpolation , pure mathematics , linear interpolation , geometry , motion (physics) , polynomial , statistics , computer science , ecology , artificial intelligence , biology
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 ⋯ + N n 3 ) from O ( N 1 3N 2 3 ⋯ N n 3 ) .