%0 Journal Article %1 scott1982advantages %A Scott, D. S. %D 1982 %I Society for Industrial & Applied Mathematics (SIAM) %J SIAM Journal on Scientific and Statistical Computing %K 15a18-eigenvalues-singular-values-and-eigenvectors 65f15-numerical-eigenvalues-eigenvectors %N 1 %P 68--75 %R 10.1137/0903006 %T The Advantages of Inverted Operators in Rayleigh–Ritz Approximations %U https://epubs.siam.org/doi/10.1137/0903006 %V 3 %X Generalized eigenvalue problems are often solved by a combination of inverse iteration and the Rayleigh–Ritz procedure. In this paper we show that significant advantages can be obtained in this context by applying the Rayleigh–Ritz procedure to an inverted operator, either explicitly while using subspace iteration or implicitly by applying the Lanczos algorithm to the inverted operator. Since the Lanczos algorithm is much more powerful than subspace iteration it should be used whenever possible. Read More: https://epubs.siam.org/doi/10.1137/0903006

@article{scott1982advantages, abstract = {Generalized eigenvalue problems are often solved by a combination of inverse iteration and the Rayleigh–Ritz procedure. In this paper we show that significant advantages can be obtained in this context by applying the Rayleigh–Ritz procedure to an inverted operator, either explicitly while using subspace iteration or implicitly by applying the Lanczos algorithm to the inverted operator. Since the Lanczos algorithm is much more powerful than subspace iteration it should be used whenever possible. Read More: https://epubs.siam.org/doi/10.1137/0903006 }, added-at = {2020-02-13T05:57:56.000+0100}, author = {Scott, D. S.}, biburl = {https://www.bibsonomy.org/bibtex/283409641cf19bcc558d46cc4555ff3d2/gdmcbain}, description = {The Advantages of Inverted Operators in Rayleigh–Ritz Approximations | SIAM Journal on Scientific and Statistical Computing | Vol. 3, No. 1 | Society for Industrial and Applied Mathematics}, doi = {10.1137/0903006}, interhash = {8e23e8ed80f21af432711e33c892ead0}, intrahash = {83409641cf19bcc558d46cc4555ff3d2}, issn = {0196-5204}, journal = {{SIAM} Journal on Scientific and Statistical Computing}, keywords = {15a18-eigenvalues-singular-values-and-eigenvectors 65f15-numerical-eigenvalues-eigenvectors}, month = mar, number = 1, pages = {68--75}, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, timestamp = {2020-02-13T05:57:56.000+0100}, title = {The Advantages of Inverted Operators in Rayleigh–Ritz Approximations}, url = {https://epubs.siam.org/doi/10.1137/0903006}, volume = 3, year = 1982 }