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1 
Uniform polynomial approximation of even and odd functions on symmetric intervalsDunham, Charles Burton January 1963 (has links)
An odd or even continuous function on a symmetric interval [a,a] can be evaluated in two different ways, each using only one uniform polynomial approximation. It is of practical importance to know which method of evaluation takes fewer arithmetic operations. This is a special case of a more general problem, which is concerned with the optimal subdivision of the interval of evaluation of a function f into subintervals, on each of which f has a uniform polynomial approximation.
In the first three chapters a method of computing the number of arithmetic operations for evaluation is developed. Expansions in Chebyshev polynomials are studied, with emphasis on the practical problem of computing coefficients, and then it is shown how the expansion in Chebyshev polynomials may be used to obtain truncation error bounds for the uniform polynomial approximation. From these bounds the required degree for the approximation and the required number of multiplications for evaluation may be easily determined. Tables of computed results are given.
In Chapter 4 theoretical results are developed from the theory of Lagrange interpolation and these results are in agreement with the computed results obtained previously. In the problem of evaluation of even and odd functions on [a,a] , use of the uniform polynomial approximation on [a,a] is advantageous unless the rate of increase of the derivative of f is rapid. In the general case of evaluation of a continuous function, use of approximations on subintervals becomes more advantageous the more rapidly the derivatives of f increase. / Science, Faculty of / Mathematics, Department of / Graduate

2 
Generating 2f orthogonal arrays.January 1990 (has links)
by Yuen Wong. / Thesis (M.Phil.)Chinese University of Hong Kong, 1990. / Chapter Chapter 1  Introduction  p.1 / Chapter Chapter 2  Basic Results  p.5 / Chapter §2.1  General Results  p.5 / Chapter §2.2  Williamson's Method  p.8 / Chapter Chapter 3  Algorithms And Subroutines  p.15 / Chapter §3.1  Introduction  p.15 / Chapter §3.2  Increasing Determinant Method  p.15 / Chapter §3.3  Williamson's Method  Direct Computation  p.21 / Chapter §3.4  Williamson's Method  Increasing Determinant  p.26 / Chapter Chapter 4  Comparisons And Recommendations On Algorithms  p.32 / Chapter §4.1  Introduction  p.32 / Chapter §4.2  Comparisons And Recommendations On IMPROV(N)  p.32 / Chapter §4.3  Comparisons And Recommendations On GENHA(N)  p.34 / Chapter §4.4  Comparisons And Recommendations On VTID(N)  p.35 / Chapter §4.5  Summary  p.37 / Chapter Chapter 5  Applications Of Hadamard Matrices  p.38 / Chapter §5.1  Hadamard Matrices And Balanced Incomplete Block Designs'  p.38 / Chapter §5.2  Hadamard Matrices And Optimal Weighing Designs  p.43 / Chapter Chapter 6  Conclusion  p.51 / References  p.52 / Appendices  p.53

3 
Projective iterative schemes for solving systems of linear equationsHawkins, John Benjamin 12 1900 (has links)
No description available.

4 
A numerical and experimental facility for wire antenna array analysis /Lemanczyk, Jerzy M. January 1978 (has links)
No description available.

5 
An information theoretic measure of algorithmic complexityWright, Lois E. January 1974 (has links)
This work is a study of an information theoretic model which is used to develop a complexity measure of an algorithm. The measure is defined to reflect the computational cost and structure of the given algorithm. In this study computational costs are expressed as the execution times of the algorithm, where the algorithm is coded as a program in a machine independent language, and analysed in terms of its representation as a pseudograph. It is shown that this measure aids in deciding which sections of the algorithm should be optimized, segmented or expressed as subprograms. The model proposed is designed to yield a measure which reflects both the program flow and computational cost. Such a measure allows an 'optimal' algorithm to be selected from a set of algorithms, all of which solve the given problem. This selection is made with a more meaningful criterion for decision than simply execution cost. The measure can also be used to further analyse a given algorithm and point to where code optimization techniques should be applied. However it does not yield a method of generating equivalent algorithms. / Science, Faculty of / Computer Science, Department of / Graduate

6 
A numerical and experimental facility for wire antenna array analysis /Lemanczyk, Jerzy M. January 1978 (has links)
No description available.

7 
Finite element solution of exterior twodimensional electrostatics problems.Hsieh, Ming Sem. January 1971 (has links)
No description available.

8 
Computer synthesis of a class of impedance matricesBudner, Alan, January 1968 (has links)
Thesis (Ph. D.)University of WisconsinMadison, 1968. / Typescript. Vita. eContent providerneutral record in process. Description based on print version record. Includes bibliography.

9 
Finite element solution of exterior twodimensional electrostatics problems.Hsieh, Ming Sem. January 1971 (has links)
No description available.

10 
On the numerical evaluation of finitepart integrals involving an algebraic singularityKutt, H. R. (Helmut Richard) 08 1900 (has links)
Thesis (PhD)Stellenbosch University, 1975. / ENGLISH ABSTRACT: Some problems of applied mathematics, for instance in the fields of
aerodynamics or electron optics, involve certain singular integrals
which do not exist classically. The problems can, however, be solved
pLovided that such integrals are interpreted as finitepart integrals.
Although the concept of a finitepart integral has existed for
about fifty years, it was possible to define it rigorously only by means
of distribution theory, developed about twentyfive years ago. But, to
the best of our knowledge, no quadrature formula for the numerical eva=
luation of finitepart integrals ha~ been given in the literature.
The main concern of this thesis is the study and discussion of.two
kinds of quadrature formulae for evaluating finitepart integrals in=
volving an algebraic singularity.
Apart from a historical introduction, the first chapter contains
some physical examples of finitepart integrals and their definition
based on distribution theory. The second chapter treats the most im=
portant properties of finitepart integrals; in particular we study
their behaviour under the most common rules for ordinary integrals.
In chapters three and four we derive a quadrature formula for equispaced
stations and one which is optimal in the sense of the Gausstype quadra=
ture. In connection with the latter formula, we also study a new class
of orthogonal polynomials. In the fifth and.last chapter we give a
derivativefree error bound for the equispaced quadrature formula. The
error quantities which are independent of the integrand were computed
for the equispaced quadrature formula and are also given. In the case
of some examples, we compare the computed error bounds with the actual
errors.
~esides this theoretical investigation df finitepart integrals,
we also computed  for several orders of the algebraic singularity
the coefficients for both of the aforesaid quadrature formulae, in
which the number of stations ranges from three up to twenty. In the
case of the equispaced quadrature fortnu1a,we give the weights and 
for int~ger order of the singularity  the coefficients for a numerical
derivative of the integrand function. For the Gausstype quadrature,
we give the stations, the corresponding weights and the coefficients of
the orthogonal polynomials.
These data are being published in a separate report [18] which
also contains detailed instructions on the use of the tables.

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