RESEARCH ARTICLE

Efficient algorithm for principal eigenpair of discrete p-Laplacian

  • Mu-Fa CHEN
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  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education, Beijing 100875, China

Received date: 15 Mar 2018

Accepted date: 09 Apr 2018

Published date: 11 Jun 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

Abstract

This paper is a continuation of the author’s previous papers [Front. Math. China, 2016, 11(6): 1379–1418; 2017, 12(5): 1023–1043], where the linear case was studied. A shifted inverse iteration algorithm is introduced, as an acceleration of the inverse iteration which is often used in the non-linear context (the p-Laplacian operators for instance). Even though the algorithm is formally similar to the Rayleigh quotient iteration which is well-known in the linear situation, but they are essentially different. The point is that the standard Rayleigh quotient cannot be used as a shift in the non-linear setup. We have to employ a different quantity which has been obtained only recently. As a surprised gift, the explicit formulas for the algorithm restricted to the linear case (p = 2) is obtained, which improves the author’s approximating procedure for the leading eigenvalues in different context, appeared in a group of publications. The paper begins with p-Laplacian, and is closed by the non-linear operators corresponding to the well-known Hardy-type inequalities.

Cite this article

Mu-Fa CHEN . Efficient algorithm for principal eigenpair of discrete p-Laplacian[J]. Frontiers of Mathematics in China, 2018 , 13(3) : 509 -524 . DOI: 10.1007/s11464-018-0697-9

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A MatLab package is also available, see the author’s homepage

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