M.Sc.

In this thesis we investigate arithmetic subroutines and round-off procedures. An error analysis of single operations in normalized floating point arithmetic leads us to the construction of an improved form of addition-subtraction subroutine. In addition the properties of several types of round-off procedures are examined (adding ½; adding random digits; dropping digits). The experimental work (using the above mentioned subroutines) with the system x• = y, y• = -x shows that the systematic accumulation of round-off error observed by Huskey is due to the type of rounding-off procedure used. Furthermore, Hartree's explanation of this effect is found to be inadequate because carrying extra digits throughout the calculations does not eliminate the systematic round-off. / Science, Faculty of / Mathematics, Department of / Graduate

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

M.Sc.

Chen, Hok. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 69-71). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Review of benchmarking methods --- p.8 / Chapter 2.1 --- Regression method --- p.9 / Chapter 2.2 --- Signal extraction method with known autocovariance of signal --- p.11 / Chapter 2.3 --- Signal extraction method with unknown autocovariance of signal --- p.16 / Chapter 3 --- Survey error modelling for MA(1) model --- p.21 / Chapter 3.1 --- A method proposed by Chow and Lin --- p.21 / Chapter 3.2 --- An alternate method proposed by Chen and Wu --- p.28 / Chapter 3.2.1 --- Original sketch for estimating 0 using annual benchmarks --- p.28 / Chapter 3.2.2 --- Nonstationary assumption for η(t) --- p.30 / Chapter 3.2.3 --- Estimating ve*ε(k) from data --- p.34 / Chapter 3.2.4 --- Simulation results --- p.36 / Chapter 4 --- Simulation Studies on Benchmarking --- p.42 / Chapter 4.1 --- Simulation procedure --- p.42 / Chapter 4.2 --- Simulation results --- p.46 / Chapter 5 --- Conclusion --- p.66 / References --- p.68

Thesis (M.S.)--West Virginia University, 2002. / Title from document title page. Document formatted into pages; contains xvii, 121, [13] p. : ill. (some col.). Vita. Includes abstract. Includes bibliographical references (p. 109-113).

Thesis (Ph. D.)--Drexel University, 2004. / Includes abstract and vita.

No description available.

Thesis (Ph.D.) -- McMaster University, 1999. / Includes bibliographical references (leaves 164-170). Also available via World Wide Web.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 189-192). Also available via the Internet.