Jongwon Lee, Journal of Internet Computing and Services, Vol. 26, No. 2, pp. 61-72, Apr. 2025
10.7472/jksii.2025.26.2.61, Full Text:  HTML
Keywords: Eigenvalue solver, Arnoldi iteration, Shift-Invert technique

Abstract

With the development of AI learning algorithms, the computation of eigenvalue and eigenvector becomes more important. Arnoldi iteration is one of the traditional techniques for finding eigenvalues, and has the characteristic of converging from the edge of the spectrum. if there is a specific area of ​interest, by applying the shift-invert technique to Arnoldi iteration, we can map the eigenvalues ​of the original spectrum to the edge of the new spectrum. It is seen that the time to find eigenvalues is dramatically shorten. In this paper, we found the eigenvalues ​of Ax = Bx for random matrices A and B with sizes of 1,000 x 1,000. It is confirmed that it converges from the edge of the spectrum in the newly mapped space, and showed a performance improvement of more than 40 times in the number of iterations and the required time.

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