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Volume 6, Issue 1
The Modified Rayleigh Quotient Iteration

Er-Xiong Jiang

J. Comp. Math., 6 (1988), pp. 80-87.

Published online: 1988-06

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  • Abstract

The Rayleigh Quotient Iteration (RQI) is a very popular method for computing eigenpairs of symmetric matrices. It is a special kind of inverse iteration method using the Rayleigh Quotient as shifts. Unfortunately, poor initial approximations may render RQI to slow convergence or even to divergence, In this paper we suggest two kinds of numbers each of which can be used instead of the Rayleigh Quotient as a shifts in the RQI. We call the iteration using the new shifts the Modified Rayleigh Quotient Iteration (MRQI). It has been proved that the MRQI always converges and its convergence rate is cubic.

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@Article{JCM-6-80, author = {Jiang , Er-Xiong}, title = {The Modified Rayleigh Quotient Iteration}, journal = {Journal of Computational Mathematics}, year = {1988}, volume = {6}, number = {1}, pages = {80--87}, abstract = {

The Rayleigh Quotient Iteration (RQI) is a very popular method for computing eigenpairs of symmetric matrices. It is a special kind of inverse iteration method using the Rayleigh Quotient as shifts. Unfortunately, poor initial approximations may render RQI to slow convergence or even to divergence, In this paper we suggest two kinds of numbers each of which can be used instead of the Rayleigh Quotient as a shifts in the RQI. We call the iteration using the new shifts the Modified Rayleigh Quotient Iteration (MRQI). It has been proved that the MRQI always converges and its convergence rate is cubic.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9500.html} }
TY - JOUR T1 - The Modified Rayleigh Quotient Iteration AU - Jiang , Er-Xiong JO - Journal of Computational Mathematics VL - 1 SP - 80 EP - 87 PY - 1988 DA - 1988/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9500.html KW - AB -

The Rayleigh Quotient Iteration (RQI) is a very popular method for computing eigenpairs of symmetric matrices. It is a special kind of inverse iteration method using the Rayleigh Quotient as shifts. Unfortunately, poor initial approximations may render RQI to slow convergence or even to divergence, In this paper we suggest two kinds of numbers each of which can be used instead of the Rayleigh Quotient as a shifts in the RQI. We call the iteration using the new shifts the Modified Rayleigh Quotient Iteration (MRQI). It has been proved that the MRQI always converges and its convergence rate is cubic.

Jiang , Er-Xiong. (1988). The Modified Rayleigh Quotient Iteration. Journal of Computational Mathematics. 6 (1). 80-87. doi:
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