Multivariate Splines for Data Fitting and Approximation

Methods for scattered data fitting using multivariate splines will be surveyed in this paper. Existence, uniqueness, and computational algorithms for these methods, as well as their approximation properties will be discussed. Some applications of multivariate splines for data fitting will be briefly explained. Some new research initiatives of scattered data fitting will be outlined. §

[1]  Ming-Jun Lai,et al.  L1 Spline Methods for Scattered Data Interpolation and Approximation , 2004, Adv. Comput. Math..

[2]  Charles K. Chui,et al.  Filling polygonal holes using C1 cubic triangular spline patches , 2000, Comput. Aided Geom. Des..

[3]  Ming-Jun Lai,et al.  Energy minimization method for scattered data Hermite interpolation , 2008 .

[4]  Gerald Farin,et al.  Triangular Bernstein-Bézier patches , 1986, Comput. Aided Geom. Des..

[5]  L. L. Schumaker,et al.  Bounds on Projections onto Bivariate Polynomial Spline Spaces with Stable Local Bases , 2002 .

[6]  Ming-Jun Lai,et al.  The Multivariate Spline Method for Scattered Data Fitting and Numerical Solutions of Partial Differential Equations , 2006 .

[7]  Larry L. Schumaker,et al.  Bernstein-Bézier polynomials on spheres and sphere-like surfaces , 1996, Comput. Aided Geom. Des..

[8]  C. K. Shum,et al.  Spherical Splines for Data Interpolation and Fitting , 2006, SIAM J. Sci. Comput..

[9]  W. Steiger,et al.  Least Absolute Deviations: Theory, Applications and Algorithms , 1984 .

[10]  Larry L. Schumaker,et al.  Fitting scattered data on sphere-like surfaces using spherical splines , 1996 .

[11]  Ming-Jun Lai,et al.  On convergence rate of the augmented Lagrangian algorithm for nonsymmetric saddle point problems , 2005 .

[12]  Larry L. Schumaker,et al.  Error bounds for minimal energy bivariate polynomial splines , 2002, Numerische Mathematik.

[13]  Larry L. Schumaker,et al.  Spline functions on triangulations , 2007, Encyclopedia of mathematics and its applications.

[14]  L. Schumaker,et al.  Scattered data fitting on the sphere , 1998 .

[15]  Ming-Jun Lai,et al.  The convergence of three L1 spline methods for scattered data interpolation and fitting , 2007, J. Approx. Theory.

[16]  John E. Lavery,et al.  Shape-preserving, multiscale fitting of univariate data by cubic L1 smoothing splines , 2000, Comput. Aided Geom. Des..

[17]  Larry L. Schumaker,et al.  PENALIZED LEAST SQUARES FITTING , 2002 .