An optimal ansatz space for moving least squares approximation on spheres An optimal ansatz space for moving least squares approximation

• Published in: Advances in computational mathematics Vol. 50; no. 6
• Main Authors: Hielscher, Ralf, Pöschl, Tim
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2024
• Subjects: Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Visualization; Sphere; Lebesgue constant; Moving least squares; 65D10; Local approximation; 65D15; Tangent space; 65D07
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-024-10201-z

We revisit the moving least squares (MLS) approximation scheme on the sphere S d - 1 ⊂ R d , where d > 1 . It is well known that using the spherical harmonics up to degree L ∈ N as ansatz space yields for functions in C L + 1 ( S d - 1 ) the approximation order O h L + 1 , where h denotes the fil...