%0 Journal Article %1 citeulike:11826287 %A Bjørstad, PetterE %A Mandel, Jan %B BIT Numerical Mathematics %D 1991 %I Kluwer Academic Publishers %K 65n30-pdes-bvps-finite-elements 35j20-variational-methods-for-second-order-elliptic-equations 15a18-eigenvalues-singular-values-and-eigenvectors 65j10-equations-with-linear-operators %N 1 %P 76--88 %R 10.1007/bf01952785 %T On the spectra of sums of orthogonal projections with applications to parallel computing %U http://dx.doi.org/10.1007/bf01952785 %V 31 %X Many parallel iterative algorithms for solving symmetric, positive definite problems proceed by solving in each iteration, a number of independent systems on subspaces. The convergence of such methods is determined by the spectrum of the sums of orthogonal projections on those subspaces, while the convergence of a related sequential method is determined by the spectrum of the product of complementary projections. We study spectral properties of sums of orthogonal projections and in the case of two projections, characterize the spectrum of the sum completely in terms of the spectrum of the product.

@article{citeulike:11826287, abstract = {{Many parallel iterative algorithms for solving symmetric, positive definite problems proceed by solving in each iteration, a number of independent systems on subspaces. The convergence of such methods is determined by the spectrum of the sums of orthogonal projections on those subspaces, while the convergence of a related sequential method is determined by the spectrum of the product of complementary projections. We study spectral properties of sums of orthogonal projections and in the case of two projections, characterize the spectrum of the sum completely in terms of the spectrum of the product.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Bj{\o}rstad, PetterE and Mandel, Jan}, biburl = {https://www.bibsonomy.org/bibtex/2573966bf40f8d07c778fa57a5c4c89c2/gdmcbain}, booktitle = {BIT Numerical Mathematics}, citeulike-article-id = {11826287}, citeulike-attachment-1 = {bjorstad_91_spectra.pdf; /pdf/user/gdmcbain/article/11826287/857910/bjorstad_91_spectra.pdf; e6ba66bd7fc38d650ab719387266812c03212f6f}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/bf01952785}, citeulike-linkout-1 = {http://link.springer.com/article/10.1007/BF01952785}, comment = {cited by Tezaur (1998, p. 6) as the basis of his presentation of abstract Schwarz methods}, doi = {10.1007/bf01952785}, file = {bjorstad_91_spectra.pdf}, interhash = {668f120065a2045a037cf0a8765a43a9}, intrahash = {573966bf40f8d07c778fa57a5c4c89c2}, keywords = {65n30-pdes-bvps-finite-elements 35j20-variational-methods-for-second-order-elliptic-equations 15a18-eigenvalues-singular-values-and-eigenvectors 65j10-equations-with-linear-operators}, number = 1, pages = {76--88}, posted-at = {2012-12-05 16:10:22}, priority = {2}, publisher = {Kluwer Academic Publishers}, timestamp = {2020-06-30T01:51:46.000+0200}, title = {{On the spectra of sums of orthogonal projections with applications to parallel computing}}, url = {http://dx.doi.org/10.1007/bf01952785}, volume = 31, year = 1991 }