A multivariant interpolation routine for a random distribution of data points

✍ Scribed by Lou Yongming; Börje Johansson

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 942 KB
• Volume: 70
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(92)90201-9

✦ Synopsis

We have developed a multivariant interpolation program which interpolates and calculates the derivatives of any function defined on a set of points randomly distributed in a three-dimensional space. Based on the Taylor expansion, the interpolation problem is transformed to find a solution of a linear equation. It is demonstrated that there is no restriction required on the data structure in the present routine and that an ill-condition problem is removed from the process when solving the linear equations by using the Gauss elimination method with complete pivoting, which interchanges both rows and columns to avoid zeros on the diagonal positions of a matrix. In the case of an ill-condition problem, the program will show which differential is valid together with its value. The generalization to higher dimensions (> 3) can readily be implemented since the formulas are derived for m dimensions without specifying its value.