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, will be defined that are analogues of polynomial B-splines. The paper includes global linear independence, polynomial reproduction, and quasi-interpolation 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 generalized multiquadrics based on a finite number of centers.
SubjectsField of Research::01 - Mathematical Sciences
- Engineering: Reports