Multivariate Splines

Univariate Splines: B splines and truncated powers on uniform mesh Univariate spline spaces Some basic properties of B splines B spline series Computation of B splines Box Splines and Multivariate Truncated Powers: Box splines Basic properties of box splines Multivariate truncated powers Box spline series Bivariate Splines on Three and Four Directional Meshes: Dimension Locally supported splines Minimal and quasi minimal supported bivariate splines Bases and approximation order Quasi Interpolation Schemes: The commutator operator Polynomial generating formulas Construction of quasi interpolants Neumann series approach Multivariate Interpolation: Interpolation by polynomials Lagrange interpolation by multivariate splines Cardinal interpolation with nonsingular Cardinal interpolation with singular Scaled cardinal interpolation Shape Preserving Approximation and Other Applications: Shape preserving approximation by box spline series Shape preserving quasi interpolation and interpolation Application of CAGD Reconstruction of gradient fields Applications to signal processing.

'This is a narration about the multivariate splines, mostly without proofs and details, with many examples treating important particular cases, with many formulas and recurrence relations, complete description of computational algorithms, and an extensive bibliography. The book would appeal to students, scientists and engineers.' B. Boyanov, Mathematical Reviews