%0 Journal Article %1 sidi1986acceleration %A Sidi, Avram %A Ford, William F. %A Smith, David A. %D 1986 %I Society for Industrial & Applied Mathematics (SIAM) %J SIAM Journal on Numerical Analysis %K 65b05-extrapolation-to-the-limit-deferred-corrections 65f10-iterative-methods-for-linear-systems %N 1 %P 178--196 %R 10.1137/0723013 %T Acceleration of Convergence of Vector Sequences %U https://epubs.siam.org/doi/10.1137/0723013 %V 23 %X A general approach to the construction of convergence acceleration methods for vector sequences is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.

@article{sidi1986acceleration, abstract = {A general approach to the construction of convergence acceleration methods for vector sequences is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.}, added-at = {2021-07-14T03:40:18.000+0200}, author = {Sidi, Avram and Ford, William F. and Smith, David A.}, biburl = {https://www.bibsonomy.org/bibtex/2b38cec9bb2dd145c4df61ea34b8e5815/gdmcbain}, doi = {10.1137/0723013}, interhash = {5faddba5d6232036400c4f2cd624f0ba}, intrahash = {b38cec9bb2dd145c4df61ea34b8e5815}, journal = {{SIAM} Journal on Numerical Analysis}, keywords = {65b05-extrapolation-to-the-limit-deferred-corrections 65f10-iterative-methods-for-linear-systems}, month = feb, number = 1, pages = {178--196}, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, timestamp = {2021-07-14T03:40:18.000+0200}, title = {Acceleration of Convergence of Vector Sequences}, url = {https://epubs.siam.org/doi/10.1137/0723013}, volume = 23, year = 1986 }