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...
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...
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...
COMPLOT is a versatile set of plot drivers designed to be used
on a Tekterminal, Calcomp, or Hewlett Packard plotter in a time-sharing
environment. Although the hardware aspects of each plotting
device are quite different, COMPLOT allows the plotting devices to
be treated as if they were the same.
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...
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.
In this thesis some methods for solving systems of
nonlinear equations are described, which do not require
calculation of the Jacobian matrix. One of these methods
is programmed to solve a parametrized system with possible
singularities. The efficiency of this method and a modified
Newton's method are compared using experimental...
This thesis describes a syntax-directed compiler-compiler
called COMCOM which has been implemented by the author on the CDC
3300 under the OS-3 operating system. The theory and terminology
of the parsing method and compiler-compilers in general are briefly
discussed. COMCOM uses Floyd's operator precedence bottom-up
parsing technique which avoids backup...
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...