Multiquadric B-splines

✍ Scribed by R.K. Beatson; N. Dyn

• Book ID: 102969293
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 852 KB
• Volume: 87
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1996.0089

✦ Synopsis

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, called -splines are defined that are analogues of polynomial B-splines. This paper includes global linear independence, polynomial reproduction, and quasiinterpolation results for the span of the -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 of -splines. These results enable us to obtain error estimates for quasi-interpolation schemes involving multiquadrics based on a finite number of centres.

1996 Academic Press, Inc.

,(x; 2k)=(x 2 +c 2 ) (2k&1)Â2 , (1.1) article no. 0089