MULTIQUADRIC B-SPLINES

Our purpose in this paper is to show that the analogy between polynomi al splines and generalized multiquadrics is very strong. In particular , combinations of multiquadrics, called psi-splines are defined that a re analogues of polynomial B-splines. This paper includes global linea r independence, polynomial reproduction, and quasi-interpolation resul ts for the span of the psi-splines on non-uniform bi-infinite meshes w hich parallel those for polynomial B-splines. There are also results c oncerning the relationship between certain semi-infinite and bi-infini te combinations of psi-splines. These results enable us to obtain erro r estimates for quasi-interpolation schemes involving multiquadrics ba sed on a finite number of centres. (C) 1996 Academic Press, Inc.