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All Journal Journal of Telematics and Informatics Indonesian Journal of Electrical Engineering and Computer Science
Muhammad Ali Raza Anjum
Army Public College of Management and Sciences, Rawalpindi, PAKISTAN
Computer Science & IT Electrical & Electronics Engineering

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One-Minute Derivation of The Conjugate Gradient Algorithm Muhammad Ali Raza Anjum
Journal of Telematics and Informatics Vol 4, No 1: March 2016
Publisher : Universitas Islam Sultan Agung

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (106.494 KB) | DOI: 10.12928/jti.v4i1.

Abstract

One of the great triumphs in the history of numerical methods was the discovery of the Conjugate Gradient (CG) algorithm. It could solve a symmetric positive-definite system of linear equations of dimension N in exactly N steps. As many practical problems at that time belonged to this category, CG algorithm became rapidly popular. It remains popular even today due to its immense computational power. But despite its amazing computational ability, mathematics of this algorithm is not easy to learn. Lengthy derivations, redundant notations, and over-emphasis on formal presentation make it much difficult for a beginner to master this algorithm. This paper aims to serve as a starting point for such readers. It provides a curt, easy-to-follow but minimalist derivation of the algorithm by keeping the sufficient steps only, maintaining a uniform notation, and focusing entirely on the ease of reader.
Adaptive System Identification using Markov Chain Monte Carlo Muhammad Ali Raza Anjum
Indonesian Journal of Electrical Engineering and Computer Science Vol 13, No 1: January 2015
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

One of the major problems in adaptive filtering is the problem of system identification. It has been studied extensively due to its immense practical importance in a variety of fields. The underlying goal is to identify the impulse response of an unknown system. This is accomplished by placing a known system in parallel and feeding both systems with the same input. Due to initial disparity in their impulse responses, an error is generated between their outputs. This error is set to tune the impulse response of known system in a way that every change in impulse response reduces the magnitude of prospective error. This process is repeated until the error becomes negligible and the responses of both systems match. To specifically minimize the error, numerous adaptive algorithms are available. They are noteworthy either for their low computational complexity or high convergence speed. Recently, a method, known as Markov Chain Monte Carlo (MCMC), has gained much attention due to its remarkably low computational complexity. But despite this colossal advantage, properties of MCMC method have not been investigated for adaptive system identification problem. This article bridges this gap by providing a complete treatment of MCMC method in the aforementioned context. DOI: http://dx.doi.org/10.11591/telkomnika.v13i1.6925 
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