Index Catalog // ScholarsArchive@OSU

Characterization of the best approximations by classic cubic splines

Creator:: Tuen, Tuen
Abstract:: This study deals specifically with classical cubic splines. Based on a lemma of John Rice, best approximation in the uniform norm by cubic splines is explored. The purpose of this study is to characterize the best approximation to a given continuous function f(x) by a cubic spline with fixed knots...
Resource Type:: Masters Thesis
Full Text:: Classic Cubic Splines (1 n 1 r. Redacted for Privacy Abstract approved: Joel Davis This study deals

Rigorous computer inversion of some linear operators

Creator:: Yungen, Walter Arthur
Abstract:: In this thesis we consider computer techniques for inverting n X n matrices and linear Fredholm integral operators of the second kind. We develop techniques which allow us to prove the existence of and find approximations to inverses for the above types of operators. In addition, we are able to...
Resource Type:: Masters Thesis
Full Text:: Abstract approved Redacted for privacy ( Dr. Joel Davis) In this thesis we consider computer

Approximation of continuous functions by Everett Splines

Creator:: Reedy, Catherine Anne
Abstract:: The approximation of a continuous function, in the maximum norm, by continuous splines in the Everett Interpolation Form is considered. The topics of characterization, uniqueness, and calculation of best approximations are investigated. Since uniqueness fails, a new vector-valued norm, which yields uniqueness, is introduced.
Resource Type:: Masters Thesis
Full Text:: from S is defined to be the set {y E Si l l y- x l l = p (x, S)}. Let S be a closed subset of a finite

A block method approach to solving the Laplace equation on a parallel computer

Creator:: Hitchcock, Paula Ann
Abstract:: This paper continues exploration in the area of programming for parallel computers. The appendix to the paper contains an extensive survey of the literature related to parallel computers and parallel programming techniques. The paper itself presents a new approach to solving the Laplace equation on a. parallel computer. A new...
Resource Type:: Masters Thesis
Full Text:: : Joel Davis This paper continues exploration in the area of programming for parallel computers. The

Numerical integration of linear integral equations with weakly discontinuous kernels

Creator:: Jacoby, Jerome Jess
Resource Type:: Masters Thesis
Full Text:: convergence for Simpson's rule is improved from first to fourth order. IÌC /;( (Joel Davis) J

A computer subroutine for the numerical solution of nonlinear Fredholm equations

Creator:: Tieman, Henry William
Resource Type:: Masters Thesis
Full Text:: Numerical Solution of Nonlinear Fredholm Equations Redacted for Privacy Abstract approved: Joel Davis

MINITRAN : an on-line function translator with capabilities for solving ordinary differential equations

Creator:: Ballance, Jeffrey David
Abstract:: A function translator is presented which was designed for interactive programs which allow functions to be defined on-line. The translator handles functions which are specified by a formula and functions which are specified as the solution to a system of differential equations.
Resource Type:: Masters Thesis
Full Text:: Abstract approved: Redacted for Privacy Joel Davis A function translator is presented which was designed

Computer techniques yielding automatic and rigorous solutions to linear and nonlinear integral equations

Creator:: Winter, Lynn Taylor
Abstract:: Interval arithmetic is applied to the problem of obtaining rigorous solutions to integral equations on a computer. The integral equations considered are the linear Fredholm equation of the second kind and the nonlinear Urysohn equation. Techniques are presented which enable the computer to find an approximate solution, prove the existence...
Resource Type:: Masters Thesis
Full Text:: approved: Redacted for privacy Joel Davis Interval arithmetic is applied to the problem of obtaining

Automated rigorous solutions to nonlinear equations

Creator:: Cullop, Paul Wayne
Abstract:: We will consider the implementation of a computer program to solve a nonlinear algebraic system of N equations and unknowns. The program involves the use of a parameter, Newton's method, and an automatic change of parameter. Also considered are rigorous error bounds for the answer. The program was implemented and...
Resource Type:: Masters Thesis
Full Text:: approved: (:/ Joel Davis We will consider the implementation of a computer program to solve a nonlinear

An investigation of bivariate approximations

Creator:: Bills, Gary Royce
Abstract:: The three important methods of approximation; interpolation, least- squares, and Chebyshev, are extended into bivariate approximations. A method of obtaining polynomial approximations for very general classes of bivariate samples is developed. Bivariate least - square approximations are reviewed and a method of developing bibariate orthogonal sequence is derived. A method...
Resource Type:: Masters Thesis
Full Text:: APPROXIMATIONS Abstract approved: Dr. Joel Davis The three important methods of approximation; interpolation

ScholarsArchive@OSU

Characterization of the best approximations by classic cubic splines

Rigorous computer inversion of some linear operators

Approximation of continuous functions by Everett Splines

A block method approach to solving the Laplace equation on a parallel computer

Numerical integration of linear integral equations with weakly discontinuous kernels

A computer subroutine for the numerical solution of nonlinear Fredholm equations

MINITRAN : an on-line function translator with capabilities for solving ordinary differential equations

Computer techniques yielding automatic and rigorous solutions to linear and nonlinear integral equations

Automated rigorous solutions to nonlinear equations

An investigation of bivariate approximations

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