This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CE 3101 Fall 2011 A Brief Introduction to Multiquadric Interpolation Background Given a set of n distinct, but otherwise arbitrary, observation locations in &lt; 2 , { ( x i , y i ) : i = 1,2,..., n } and given the values of a real function at these locations { z i = z ( x i , y i ) : i = 1,2,..., n } the construction of a function F ( x , y ) mapping &lt; 2 &lt; and satisfying F ( x i , y i ) = z i i = 1,2,... n (1) is called scattered data interpolation . An important class 1 of scattered data interpolation methods is known as radial basis function interpolation (e.g. Madych and Nelson [1988] and Powell [1990]). The general class of radial basis function interpolation includes kriging (e.g. Isaaks and Srivastava [1989]), thin plate splines (Duchon [1978] ), and multiquadric interpolation (Hardy [1990] ), to name a few popular specific cases. Furthermore, radial basis function methods have been found to be pragmatically superior to many other published methods of scattered data interpolation (e.g. Franke [1982] ). Multiquadric Interpolation Multiquadric interpolation is one of the more popular methods 2 of radial basis function interpolation. Mul tiquadric interpolants take the form F ( x , y ) = + n X i = 1 w i ( d i ( x , y )) (2) is an unknown coefficient 3 computed by applying (1). (This is discussed in more detail below.) w i is an unknown coefficient associated with observation i , which is computed by applying (1). (This is, which is computed by applying (1)....
View
Full
Document
This note was uploaded on 02/15/2012 for the course CIVIL 3101 taught by Professor Barnes during the Spring '11 term at Minnesota.
 Spring '11
 Barnes

Click to edit the document details