MULTISCALE ANALYSIS IN SOBOLEV SPACES ON THE SPHERE

作者：Le Gia Q T^*; Sloan I H; Wendland H

来源：SIAM Journal on Numerical Analysis, 2010, 48(6): 2065-2090.

DOI：10.1137/090774550

• multiscale
• approximation
• interpolation
• radial basis functions
• unit sphere

We consider a multiscale approximation scheme at scattered sites for functions in Sobolev spaces on the unit sphere S(n). The approximation is constructed using a sequence of scaled, compactly supported radial basis functions restricted to S(n). A convergence theorem for the scheme is proved, and the condition number of the linear system is shown to stay bounded by a constant from level to level, thereby establishing for the first time a mathematical theory for multiscale approximation with scaled versions of a single compactly supported radial basis function at scattered data points.

• 出版日期2010