TRUE DAN GHOST BREAKDOWN PADA ALGORITMA LANCZOS TIPE A4/ORTHORES DALAM SISTEM LINIER BERDIMENSI TINGGI

Maharani Maharani (University of Jendearl Soedirman, Purwokerto)

Procediamath
Vol 1, No 1 (2017)

Lanczos method is an iterative method used to find the solution of a system of linear equations. Currently, the Lanczos method has been expanded and modified into several types. One type that has been considerably implemented is the Lanczos-type  (Orthores algorithm). This research examines the Orthores derivation algorithm by applying Formal Orthogonal Polynomials (FOPs). The Lanczos algorithm is very effective for solving systems of high-dimensional linear equations (SLEs). However, it is very susceptible to high iteration use or to orthogonal polynomials. This phenomenon is commonly called breakdown. Breakdown occurs because of the division by zero when the computation process takes place, and thus the algorithm halts.. In this study, the algorithm was implemented in some variety of SLEs, ranging from1000 to 10.000 dimensions.  Keywords : Lanczos method, formula A4/Orthores, algorithm A4/Orthores, FOPs, breakdown.