%0 Journal Article %1 Zulehner_2001 %A Zulehner, Walter %D 2001 %I American Mathematical Society (AMS) %J Mathematics of Computation %K 65f08-preconditioners-for-iterative-methods 76d07-stokes-and-related-oseen-etc-flows %N 238 %P 479--506 %R 10.1090/s0025-5718-01-01324-2 %T Analysis of iterative methods for saddle point problems: a unified approach %U https://doi.org/10.1090%2Fs0025-5718-01-01324-2 %V 71 %X In this paper two classes of iterative methods for saddle point problems are considered: inexact Uzawa algorithms and a class of methods with symmetric preconditioners. In both cases the iteration matrix can be transformed to a symmetric matrix by block diagonal matrices, a simple but essential observation which allows one to estimate the convergence rate of both classes by studying associated eigenvalue problems. The obtained estimates apply for a wider range of situations and are partially sharper than the known estimates in literature. A few numerical tests are given which confirm the sharpness of the estimates.

@article{Zulehner_2001, abstract = { In this paper two classes of iterative methods for saddle point problems are considered: inexact Uzawa algorithms and a class of methods with symmetric preconditioners. In both cases the iteration matrix can be transformed to a symmetric matrix by block diagonal matrices, a simple but essential observation which allows one to estimate the convergence rate of both classes by studying associated eigenvalue problems. The obtained estimates apply for a wider range of situations and are partially sharper than the known estimates in literature. A few numerical tests are given which confirm the sharpness of the estimates. }, added-at = {2019-05-03T08:44:46.000+0200}, author = {Zulehner, Walter}, biburl = {https://www.bibsonomy.org/bibtex/226bfa302d4b392717fc32e49c4dbee74/gdmcbain}, doi = {10.1090/s0025-5718-01-01324-2}, interhash = {eb974a533f4fbaf1cc0e60b952916346}, intrahash = {26bfa302d4b392717fc32e49c4dbee74}, journal = {Mathematics of Computation}, keywords = {65f08-preconditioners-for-iterative-methods 76d07-stokes-and-related-oseen-etc-flows}, month = may, number = 238, pages = {479--506}, publisher = {American Mathematical Society ({AMS})}, timestamp = {2024-03-27T01:13:33.000+0100}, title = {Analysis of iterative methods for saddle point problems: a unified approach}, url = {https://doi.org/10.1090%2Fs0025-5718-01-01324-2}, volume = 71, year = 2001 }