Multiquadric B-splines
Our purpose in this paper is to show that the analogy between polynomial splines and generalized multiquadrics is very strong. In particular, combinations of multiquadrics, calledψ-splines are defined that are analogues of polynomial B-splines. This paper includes global linear independence, polynom...
Saved in:
| Published in | Journal of approximation theory Vol. 87; no. 1; pp. 1 - 24 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.10.1996
|
| Online Access | Get full text |
Cover
Loading…
| Summary: | Our purpose in this paper is to show that the analogy between polynomial splines and generalized multiquadrics is very strong. In particular, combinations of multiquadrics, calledψ-splines are defined that are analogues of polynomial B-splines. This paper includes global linear independence, polynomial reproduction, and quasi-interpolation results for the span of theψ-splines on non-uniform bi-infinite meshes which parallel those for polynomial B-splines. There are also results concerning the relationship between certain semi-infinite and bi-infinite combinations ofψ-splines. These results enable us to obtain error estimates for quasi-interpolation schemes involving multiquadrics based on a finite number of centres. |
|---|---|
| ISSN: | 0021-9045 1096-0430 |
| DOI: | 10.1006/jath.1996.0089 |