• Journal of Korea Society of Industrial Information Systems
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• v.7 no.5
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• pp.59-66
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• 2002

Many important scientific and engineering problems require the computation of a small number of eigenvalues for large nonsymmetric matrices. The biorthogonal Lanczos method is one of the methods to solve that problem, but it faces serious breakdown problems. In this paper, we introduce a modified biorthogonal Lanczos method to find a few eigenvalues of a large sparse nonsymmetric matrix. The proposed method generates reduction matrices that are similar to those generated by the standard biorthogonal Lanczos method. We prove that the breakdown conditions of our method are less stringent than the standard method. We then implement the modified biorthogonal Lanczos method on the CRAY machine and discuss the decreased breakdown conditions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.11
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• pp.1852-1861
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• 1997

An enhanced subspace iteration algorithm has been developed to solve eigenvalue problems reliably and efficiently. Basic subspace iteration algorithm has been improved by eliminating recalculation of converged eigenvectors, using Krylov sequence as initial vectors and incorporating with shifting techniques. The number of iterations and computational time have been considerably reduced when compared with the original one, and reliability for catching copies of the multiple roots has been retained successfully. Further research would be required for mathematical justification of the present method.

• Journal of Korea Society of Industrial Information Systems
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• v.4 no.4
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• pp.88-93
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• 1999

Several Iterative methods are considered, Gram-Schmidt algerian for thin orthogonalization and Lanczos methodfor a few extreme eigenvalues. For these methods, a variants of method is derived for which only one synchronization point per on iteration is required; that is one global communication in a message passing distributed-memory machine per one iteration is required The variant is called restructured method, and restructured method has better parallel properties to the conventional method.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 2000.11a
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• pp.483-489
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• 2000

슈퍼컴퓨터는 여러 분야에서 많이 이용되고 있으며 특히 과학과 공학 분야에서 해결하려는 응용문제들은 더욱 빠른 컴퓨터에 대한 요구가 보다 많아지고 있다. 이미 단일 프로세서로는 그 요구를 충족시킬 수 없으며 따라서 병렬처리 기법의 도입이 불가피하다. 컴퓨터는 하드웨어만으로 모든 것이 해결되지 않는다. 하드웨어적인 특징을 극대화할 수 있는 알고리즘과 프로그램 등 소프트웨어 개발이 필수적이다. 본 논문에서는 아주 큰 행렬의 극한의 고유치(extreme eigenvalue)를 구하는 란초스(Lanczos) 알고리즘, 또한 아주 큰 선형시스템의 해를 구하는 GMRES방법에 대하여 병렬알고리즘을 제안하고 message-passing 병렬처리 컴퓨터에서 얼마나 효과적으로 수행할 수 있는지 분석한다. 초병렬 컴퓨터(MPP)인 Cray T3E는 128개의 PE(Processing Element)로 구성되어 있는데 사용하는 PE의 수에 따라 병렬알고리즘의 성능분석을 하였다.