Browsing by Author "Bhavsar, V., C."
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Item Design and analysis of parallel Monte Carlo algorithms(1985) Bhavsar, V., C.; Isaac, J., R.This paper demonstrates that the potential of intrinsic parallelism in Monte Carlo methods, which has remained essentially untapped so far, can be exploited to implement these methods efficiently on SIMD and MIMD computers. Two basic static and dynamic computation assignment schemes are proposed for assigning the primary estimate computations (PECs) to processors in a parallel computer. These schemes can be used to design parallel Monte Carlo algorithms for many applications. The time complexity analyses of static computation assignment (SCA) schemes are carried out using some results from order statistics, whereas those of dynamic computation assignment (DCA) schemes are carried out using results from order statistics, renewal and queuing theories. It is shown that for smaller number of processors, linear speedup can be achieved with the SCA schemes and the speedup almost equal to the number of processors can be achieved with the DCA schemes. Some computational results for Monte Carlo solutions of Laplace*s equation are given to illustrate the performance of the various SCA and DCA schemes.Item Fractal Images from z <- z a + c In the Complex z-Plane(1990) Gujar, U., G.; Bhavsar, V., C.; Vangala, N.The transformation function z <- z[superscript a] + c is used for generating fractal images in the complex z-plane. When a is a positive integer the fractal image has a lobular structure with a major lobes. When a is a negative integer the image has a planetary configuration consisting of a central planet with | a | major satellite structures. For non-integer values of a, additional embryonic lobular/satellite structures, proportional in size to the fractional part of a, are observed. Based on the extensive experimentation, six conjectures regarding the number of major as well as embryonic lobular/satellite structures, their positions and angular spaces are formulated.Item Generation of discrete random variables on vector computers for Monte Carlo simulations(1990) Sarno, R.; Bhavsar, V., C.; Hussein, E., M., A.The paper reviews existing methods for generating discrete random variables and their suitability for vector processing. A new method for generating discrete random variables for use in vectorized Monte Carlo simulations is presented. The method uses the concept of importance sampling and generates random variables by employing uniform distribution to speedup the computation. The sampled random variables are subsequently adjusted so that unbiased estimates are obtained. The method preserves both mean and variance of the original distribution. It is demonstrated that the method requires simpler coding and shorter execution time for both scalar and vector processing, when compared with other existing methods. The vectorization speedup of the method is demonstrated on an IBM 3090-180 machine with a vector facility. Keywords: discrete random variables, importance sampling, Monte Carlo simulation, parallel processing, supercomputing, vector processingItem Time complexity of sequential and parallel Monte Carlo solution of linear equations(1987) Bhavsar, V., C.The Monte Carlo method proposed by von Neumann and Ulam for solving linear equations is considered in this paper. It is shown that the primary estimate computation processes in this method can be viewed as the realizations of an absorbing Markov chain. Subsequently, the time complexity analysis of the algorithm is carried out using some results from the absorbing Markov chain theory. Two techniques, proper transition probability assignments and the truncation of random walks, are discussed for the time complexity reduction. Finally, the various schemes recently presented for the development of parallel Monte Carlo algorithms are shown to be applicable in implementing the method on parallel computers. It is shown that the time complexity of the method for estimating the solutions of a system of Ν linear equations on Ν·Κ processors, using Κ primary estimates for each of the unknowns, is independent of N.Item Vectorization techniques for algebraic fractals(1990) Bhavsar, V., C.; Gujar, U., G.; Vangala, N.Algebraic fractals generated from the self-squared transformation function z <— z[superscript 2] + c, where z and c are complex quantities, have been discussed extensively in the literature. The process of generating these fractal images, being iterative in nature, is computationally intensive. In this paper we propose and study three vectorization techniques for generating algebraic fractals from z <— z[superscript 2] + c, namely, use of long vectors, short vectors and short vectors with replenishment. The speedups obtained by vectorization of all these techniques on IBM 3090-180VF, which has a vector facility, are presented. It is observed that the technique of using short vectors with replenishment is the best.