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Diagonal Scalings of the Laplacian as Preconditioners for Other Elliptic Differential Operators (Classic Reprint) - Softcover
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Excerpt from Diagonal Scalings of the Laplacian as Preconditioners for Other Elliptic Differential Operators
The spaces defined by and are both A-orthogonal and C-orthogonal to one another, and together they span all of R. The technique of expressing a given vector as a sum of vectors from each space will be used in the proofs throughout the paper.
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This 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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- PublisherForgotten Books
- Publication date2024
- ISBN 10 1332120199
- ISBN 13 9781332120192
- BindingPaperback
- LanguageEnglish
- Number of pages29
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Diagonal Scalings of the Laplacian as Preconditioners for Other Elliptic
Print on DemandSeller: Forgotten Books, London, United Kingdom
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Paperback. Condition: New. Print on Demand. This book explores the use of diagonal scalings of the Laplacian matrix as a method for preconditioning (improving the conditioning of) matrices that arise from second-order elliptic differential equations. The author proves that for a class of diffusion equations with discontinuous diffusion coefficients, the optimal diagonal scaling is the identity matrix as the mesh size approaches zero. This is in contrast to the case of diffusion equations with continuously varying coefficients, where numerical evidence suggests that the optimal diagonal scaling is approximately equal to the square root of the diagonal of the matrix. The book provides a theoretical framework for understanding the behavior of diagonal scalings of the Laplacian as preconditioners and offers insights into the relationship between the properties of the diffusion equation and the effectiveness of this preconditioning technique. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332120192_0
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Diagonal Scalings of the Laplacian as Preconditioners for Other Elliptic Differential Operators Classic Reprint
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LX-9781332120192
Quantity: 15 available
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Diagonal Scalings of the Laplacian as Preconditioners for Other Elliptic Differential Operators Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
Seller rating 5 out of 5 stars
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LX-9781332120192
Quantity: 15 available