Minimal Norm Constrained Interpolation

<p>In computational fluid dynamics and in CAD/CAM a physical boundary, usually known only discreetly (say, from a set of measurements), must often be approximated. An acceptable approximation must, of course, preserve the salient features of the data (convexity, concavity, etc.) In this dissertation we compute a smooth interpolant which is locally convex where the data are locally convex and is locally concave where the data are locally concave.</p> <p>Such an interpolant is found by posing and solving a minimization problem. The solution is a piecewise cubic polynomial. We actually solve this problem indirectly by using the Peano kernel theorem to recast this problem into an equivalent minimization problem having the second derivative of the interpolant as the solution.</p> <p>We are then led to solve a nonlinear system of equations. We show that with Newton's method we have an exceptionally attractive and efficient method for solving this nonlinear system of equations.</p> <p>We display examples of such interpolants as well as convergence results obtained by using Newton's method. We list a FORTRAN program to compute these shape-preserving interpolants.</p> <p>Next we consider the problem of computing the interpolant of minimal norm from a convex cone in a normed dual space. This is an extension of de Boor's work on minimal norm unconstrained interpolation.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics & Statistics

Year dc:date.available

1985

Author dc:creator

• Irvine, Larry Dean

Contributors dc:contributor

• Philip W. Smith
• John Swetits
• James L. Schwing

• Computational fluid dynamics
• CAD/CAM
• Boundary
• Measurements
• Cubic polynomial
• Fluid Dynamics
• Mathematics

Statement dc:rights

• <p>In Copyright. URI: <a href="http://rightsstatements.org/vocab/InC/1.0/">http://rightsstatements.org/vocab/InC/1.0/</a> This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).</p>

Repository record dc:identifier

https://digitalcommons.odu.edu/mathstat_etds/100

OAI identifier oai:identifier

oai:digitalcommons.odu.edu:mathstat_etds-1093