Pi, Epsilon, With Matlab: Random And Rational Sequences With Scope In Supercomputing Era

Description S. K. Sen, Department of Mathematical Sciences, Florida Institute of Technology, USA, and R.P. Agarwal, Department of Mathematics, Texas A&M University-Kingsville, USA The Authors present some characters of three famous irrational numbers pi (the area of the circle of unit radius). Epsilon (the exponential function with argument 1) and Phi (the golden ratio). along with their formulas and their variable precision computations in Matlab.                                                            They also explore the possible use and efficacy of each of these numbers as random sequence sources for solving real world problems specifically in the ultra-high speed computing era. in addition, algorithms are described for the best absolute rational approximation of these numbers of these numbers and their usage in error-free computations. The concerned programs/commands are included, written in high level, user friendly, and globally available programming language Matlab. This volume is intended to be a useful reference book for students of engineering and science courses that involve numerical computations including error-free computations and those underlying evolutionary approaches genetic and randomized algorithms for optimization and for other applications.