Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498308 | Linear Algebra and its Applications | 2005 | 22 Pages |
Abstract
A cardinal spline Hermite interpolation problem is posed by specifying values, and m â 1 derivatives, m ⩾ 1, at uniformly spaced knots tk; it may be solved by means of a generalized spline function w(t) (a standard spline function when m = 1), piecewise a polynomial of degree n â 1 = 2m + p â 1, p ⩾ 0, with w(j)(t) continuous across the knots for j = 0, 1, 2, â¦Â , m + p â 1. The problem is studied here for p > 0 in the context of an (m + p)-dimensional system of linear recursion equations satisfied by the values of the m-th through m + p â 1-st derivatives of w(t) at the knots, whose homogeneous term involves a p Ã p matrix A . In the case m = 1 we relate the characteristic polynomial of A and certain controllability notions to the standard B-spline and we proceed to show how systems-theoretic ideas can be used to generate systems of basis splines for higher values of m.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
M. Renardy, D.L. Russell,