Diagonal Scalings of the Laplacian as Preconditioners for Other Elliptic Differential Operators Anne Greenbaum

Diagonal Scalings of the Laplacian as Preconditioners for Other Elliptic Differential Operators by Anne Greenbaum
September 27th 2015 | Paperback | PDF, EPUB, FB2, DjVu, AUDIO, mp3, RTF | 28 pages | ISBN: 9781332120192 | 10.74 Mb

Excerpt from Diagonal Scalings of the Laplacian as Preconditioners for Other Elliptic Differential OperatorsWe consider the use of diagonal scalings of the Laplacian matrix as preconditioners for matrices arising from other second order self-adjointMoreExcerpt from Diagonal Scalings of the Laplacian as Preconditioners for Other Elliptic Differential OperatorsWe consider the use of diagonal scalings of the Laplacian matrix as preconditioners for matrices arising from other second order self-adjoint elliptic differential operators.

It is proved that if a diffusion operator with a piecewise constant but discontinuous diffusion coefficient is preconditioned by a diagonal scaling of the Laplacian, then, in the limit as the mesh size goes to zero, the optimal diagonal scaling is just the identity. This is in contrast to the case in which the diffusion coefficient is smoothly varying, in which case numerical evidence suggests that the optimal diagonal scaling is approximately equal to the square root of the diagonal of the matrix.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books.

Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully- any imperfections that remain are intentionally left to preserve the state of such historical works.

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