Local spline approximation methods

DOI10.1016/0021-9045(75)90091-XzbMath0315.41011OpenAlexW2075157922MaRDI QIDQ1221064

Tom Lyche, Larry L. Schumaker

Publication date: 1975

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(75)90091-x

Mathematics Subject Classification ID

Multidimensional problems (41A63) Spline approximation (41A15)

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Cites Work

• Spline approximation by quasiinterpolants
• On Polya frequency functions. IV: The fundamental spline functions and their limits
• An identity for spline functions with applications to variation diminishing spline approximation
• On uniform approximation by splines
• On calculating with B-splines
• Error bounds for spline and L-spline interpolation
• On finite element approximations to time-dependent problems
• On uniform approximation by certain generalized spline functions
• $L^\infty $-Multivariate Approximation Theory
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item