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Numerical Analysis
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This report contains a description of the typical topics covered in a two-semester sequence in Numerical Analysis, and describes the accuracy, efficiency and robustness of these algorithms.Abstract:
Introduction. Mathematical approximations have been used since ancient times to estimate solutions, but with the rise of digital computing the field of numerical analysis has become a discipline in its own right. Numerical analysts develop and study algorithms that provide approximate solutions to various types of numerical problems, and they analyze the accuracy, efficiency and robustness of these algorithms. As technology becomes ever more essential for the study of mathematics, learning algorithms that provide approximate solutions to mathematical problems and understanding the accuracy of such approximations becomes increasingly important. This report contains a description of the typical topics covered in a two-semester sequence in Numerical Analysis.read more
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Development of a computer simulation model for processing food in a microwave assisted thermal sterilization (MATS) system
TL;DR: The microwave assisted thermal sterilization computer simulation model (MATS-CSM) as discussed by the authors was developed to improve the previous computer simulation models for the microwave-assisted thermal sterilisation system, which included determination of optimum heating time step, evaluation of electromagnetic field distribution and resulting heating pattern in food, and experimental validation of heating patterns.
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An information-theoretic criterion for intrasubject alignment of FMRI time series: motion corrected independent component analysis
TL;DR: It is suggested MCICA represents a robust and reliable method for preprocessing of fMRI time-series corrupted with motion and may be corrected by determining the linear combination of spatial transformations of the motion-corrupted volume that maximizes the proposed criterion.
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On a class of q-Bernoulli and q-Euler polynomials
TL;DR: In this article, a class of generalized Bernoulli polynomials and Euler polynomial based on the q-integers is introduced and investigated, and a q-analogues of well-known formulas are derived.
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On the approximation of infinite optimization problems with an application to optimal control problems
TL;DR: In this article, the authors derived convergence results for the optimal solutions and the optimal values of the approximating problems under the assumption of a first order necessary and a second order sufficient optimality condition.
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Incorporation of Variable-Speed Pumping in Multiobjective Genetic Algorithm Optimization of the Design of Water Transmission Systems
TL;DR: In this paper, a pump power estimation method, developed using a false position method based optimization approach, is proposed to incorporate variable speed pumps in the conceptual design or planning of water transmission systems (WTSs), using optimi...