Interpolation and Approximation

Description

In this paper, there are three chapters. The first chapter discusses interpolation. Here a theorem about the uniqueness of the solution to the general interpolation problem is proven. Then the problem of how to represent this unique solution is discussed. Finally, the error involved in the interpolation and the convergence of the interpolation process is developed. In the second chapter a theorem about the uniform approximation to continuous functions is proven. Then the best approximation and the least squares approximation (a special case of best approximation) is discussed. In the third chapter orthogonal polynomials as discussed as well as bounded ... continued below

iii, 53 leaves

Creation Information

Lal, Ram May 1977.

Context

This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 39 times . More information about this thesis can be viewed below.

Who

People and organizations associated with either the creation of this thesis or its content.

Rights Holder

For guidance see Citations, Rights, Re-Use.

• Lal, Ram

Provided By

UNT Libraries

The UNT Libraries serve the university and community by providing access to physical and online collections, fostering information literacy, supporting academic research, and much, much more.

What

Descriptive information to help identify this thesis. Follow the links below to find similar items on the Digital Library.

Description

In this paper, there are three chapters. The first chapter discusses interpolation. Here a theorem about the uniqueness of the solution to the general interpolation problem is proven. Then the problem of how to represent this unique solution is discussed. Finally, the error involved in the interpolation and the convergence of the interpolation process is developed. In the second chapter a theorem about the uniform approximation to continuous functions is proven. Then the best approximation and the least squares approximation (a special case of best approximation) is discussed. In the third chapter orthogonal polynomials as discussed as well as bounded linear functionals in Hilbert spaces, interpolation and approximation and approximation in Hilbert space.

iii, 53 leaves

Identifier

Unique identifying numbers for this thesis in the Digital Library or other systems.

Collections

This thesis is part of the following collection of related materials.

UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

What responsibilities do I have when using this thesis?

When

Dates and time periods associated with this thesis.

• May 1977

Added to The UNT Digital Library

• May 10, 2015, 6:16 a.m.

Description Last Updated

• June 17, 2016, 12:02 p.m.

Yesterday: 0
Past 30 days: 0
Total Uses: 39

Interact With This Thesis

Here are some suggestions for what to do next.