Title :
Convergence Analysis of Jacobi Iterative Method Using Logarithmic Number System
Author :
Huang, Peng ; Teng, Daniel H Y ; Wahid, Khan ; Ko, Seok-Bum
Author_Institution :
Dept. of Electr. & Comput. Eng., Saskatchewan Univ., Saskatoon, SK
Abstract :
This paper presents convergence analysis of Jacobi iterative method using logarithmic number system (LNS) for solving linear systems, where multiplications and divisions are replaced with additions and subtractions, respectively. Two major factors are identified and considered in our convergence analysis. First, in any hardware architecture for Jacobi iterative method, only a set of unknowns can be processed in parallel due to the constraint of hardware resources. Secondly, the conversions of logarithm-to-floating-point and floating-to-logarithm introduce additional error. The convergence analysis demonstrates to what extent the hardware resource constraints and additional conversion error affect the convergence of Jacobi iterative method.
Keywords :
convergence of numerical methods; error analysis; floating point arithmetic; iterative methods; mathematics computing; Jacobi iterative method; convergence analysis; conversion error; logarithm-to-floating-point; logarithmic number system; Circuits; Convergence; Error analysis; Error correction; Hardware; Iterative methods; Jacobian matrices; Linear systems; Numerical analysis; Read only memory; Jacobi iterative method; logarithmic number system (LNS);
Conference_Titel :
Computer and Information Science, 2008. ICIS 08. Seventh IEEE/ACIS International Conference on
Conference_Location :
Portland, OR
Print_ISBN :
978-0-7695-3131-1
DOI :
10.1109/ICIS.2008.97