| Abstract | 第1-7页 |
| 摘要 | 第7-11页 |
| 1 Introduction | 第11-19页 |
| ·Spline interpolation and Hermite interpolation | 第11-14页 |
| ·Radial basis function interpolation | 第14-16页 |
| ·Scientific Applications | 第16-17页 |
| ·Computer Aided Geometric Design (CAGD) | 第17-19页 |
| 2 B-splines Theories and Applications | 第19-50页 |
| ·Cubic Splines | 第19-27页 |
| ·Cubic-spline derivation | 第21-27页 |
| ·Constructing the B-splines Basis functions | 第27-33页 |
| ·Approached Representations of Continuous Linear Functions | 第33-37页 |
| ·Approached representation of linear functions | 第33-34页 |
| ·Optimal approximate functions | 第34-35页 |
| ·Exact approximate Functions for splines functions | 第35-37页 |
| ·Interpolation methods constructed by B-spline basic function | 第37-50页 |
| ·Local Interpolation Modelling of Quadratic B-Spline function and it's Application for Stock Market | 第37-43页 |
| ·Basic function determination | 第37-38页 |
| ·B-spline basic function fitting modelling and forecast question | 第38-40页 |
| ·Local Interpolation modelling by quadratic B-splines | 第40-42页 |
| ·Application for stock market: | 第42-43页 |
| ·Predicting Arithmetic of Lagrange Interpolation Modelling and it's Application for Stock Market | 第43-46页 |
| ·Lagrange interpolation | 第44-46页 |
| ·Application for stock market | 第46页 |
| ·Quadratic B-Spline curves and Surfaces | 第46-50页 |
| ·Quadratic B-spline curves | 第46-48页 |
| ·Quadratic B-Spline Surface | 第48-50页 |
| 3. Statistic histogram curves Approximation based on area constraint | 第50-59页 |
| ·Piecewise cubic spline interpolation | 第50-52页 |
| ·Piecewise cubic Hermite interpolation and Applications | 第52-59页 |
| ·Piecewise-cubic Hermite Interpolation | 第52-53页 |
| ·Area constraint (or computing method) | 第53-57页 |
| ·Graphical Application | 第57-59页 |
| 4. Large Scattered Data Interpolation By Radial Basis Fuction | 第59-73页 |
| ·Scattered data interpolation | 第59-62页 |
| ·Positive Definite Case | 第60-61页 |
| ·Positive Definite Matrices | 第61-62页 |
| ·Radial basis function interpolation | 第62-66页 |
| ·Solution of system | 第65-66页 |
| ·Graphical Application | 第66页 |
| ·Modification of Radial Basis Functions | 第66-73页 |
| ·Approximate interpolants | 第66-67页 |
| ·Approximate interpolation properties | 第67-70页 |
| ·Numerical examples | 第70-73页 |
| 5. Box Spline Surfaces | 第73-86页 |
| ·definitions of box splines | 第73-77页 |
| ·Basic properties of Box splines | 第77-78页 |
| ·Translates of Box splines | 第78-80页 |
| ·Derivatives and polynomials properties | 第80-81页 |
| ·Convexity | 第81-82页 |
| ·Subdivision | 第82-84页 |
| ·Matching Box Spline and Tensor Product B-spline Surfaces | 第84-86页 |
| ·Tensor Product B-spline | 第84页 |
| ·Derivatives of box spline surfaces | 第84-86页 |
| 6. Conclusion | 第86-87页 |
| References | 第87-93页 |
| PUBLICATIONS | 第93-94页 |
| Acknowledgments | 第94页 |
