published_or_final_version / Mathematics / Master / Master of Science

published_or_final_version / Mathematics / Master / Master of Philosophy

The realization of high-speed numeric computation is a sought-after commodity for real world applications, including high-speed scientific computation, digital signal processing, and embedded computers. An example of this is the generation of elementary functions, such as sin( ) x , x e and log( ) x . Sasao, Butler and Reidel [Ref. 1] developed a high speed numeric function generator using a look-up table (LUT) cascade. Their method used a piecewise linear segmentation algorithm to generate the functions [Ref. 1]. In this thesis, two alternative segmentation algorithms are proposed and compared to the results of Sasao, Butler and Reidel [Ref.1]. The first algorithm is the Constant Approximation. This algorithm uses lines of slope zero to approximate a curve. The second algorithm is the power-of-2-approximation. This method uses 2i x to approximate a curve. The constant approximation eliminates the need for a multiplier and adder, while the power-of-2-approximations eliminates the need for multiplier, thus improving the computation speed. Tradeoffs between the three methods are examined. Specifically, the implementation of the piecewise linear algorithm requires the most amount of hardware and is slower than the other two. The advantage that it has is that it yields the least amount of segments to generate a function. The constant approximation requires the most amount of hardware to realize a function, but is the fastest implementation. The power-of-2 approximation is an intermediate choice that balances speed and hardware requirements.

by Lau Siu Chung. / "April 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 97-102). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Thesis (Ph.D.)--York University, 2004. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 160-165). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ99262

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 by counting alternating extreme points of its error function E(t). / Graduation date: 1991

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Statistics and Biostatistics." Includes bibliographical references (p. 60-61).

Thesis (M. Sc.)--University of Hong Kong, 1969. / Typewritten.

published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy