A PREEMPTIVE RESTARTING APPROACH TO BEATING THE INHERENT INSTABILITY OF LANCZOS-TYPE ALGORITHMS

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FAROOQ M.; SALHI A.

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Paper Information

Journal: IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE Year:2013 | Volume:37 | Issue:A3 (SPECIAL ISSUE-MATHEMATICS) Page(s): 349-358

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Information Journal Paper

Title

A PREEMPTIVE RESTARTING APPROACH TO BEATING THE INHERENT INSTABILITY OF LANCZOS-TYPE ALGORITHMS

Author(s)

FAROOQ M. | SALHI A. | Issue Writer Certificate

Keywords

LANCZOS ALGORITHM

SYSTEMS OF LINEAR EQUATIONS

FORMAL ORTHOGONAL POLYNOMIALS

RESTARTING

SWITCHING

BREAKDOWN

Abstract

Lanczos-type algorithms are well known for their inherent instability. They typically BREAKDOWN occurs when relevant orthogonal polynomials do not exist. Current approaches to curing BREAKDOWN rely on jumping over the non-existent polynomials to resume computation. This may have to be used many times during the solution process. We suggest an alternative to jumping, which consists of RESTARTING the algorithms that fail. Three different strategies can be taken: (ST1) RESTARTING following BREAKDOWN of the algorithm in use; (ST2) pre-emptive RESTARTING after a fixed number of iterations; (ST3) RESTARTING when near BREAKDOWN is detected through monitoring. We describe a RESTARTING framework with a generic algorithm that invokes one or the other of the three strategies suggested. Four of the most prominent recently developed Lanczos-type algorithms namely, A4, A12, A5/B10 and A8/B10 will be presented and then deployed in the RESTARTING framework. However, we will only report on results obtained with strategy ST2 as it is the only viable one at the moment.

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APA: Copy

FAROOQ, M., & SALHI, A.. (2013). A PREEMPTIVE RESTARTING APPROACH TO BEATING THE INHERENT INSTABILITY OF LANCZOS-TYPE ALGORITHMS. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, 37(A3 (SPECIAL ISSUE-MATHEMATICS)), 349-358. SID. https://sid.ir/paper/618328/en

Vancouver: Copy

FAROOQ M., SALHI A.. A PREEMPTIVE RESTARTING APPROACH TO BEATING THE INHERENT INSTABILITY OF LANCZOS-TYPE ALGORITHMS. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE[Internet]. 2013;37(A3 (SPECIAL ISSUE-MATHEMATICS)):349-358. Available from: https://sid.ir/paper/618328/en

IEEE: Copy

M. FAROOQ, and A. SALHI, “A PREEMPTIVE RESTARTING APPROACH TO BEATING THE INHERENT INSTABILITY OF LANCZOS-TYPE ALGORITHMS,” IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, vol. 37, no. A3 (SPECIAL ISSUE-MATHEMATICS), pp. 349–358, 2013, [Online]. Available: https://sid.ir/paper/618328/en

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