Support Theory for Preconditioning

By E. Boman, Bruce Hendrickson. 2003

123 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mechanics, Computational Theory and Mathematics

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In Atomic and Molecular Physics, and Optics

In Computational Mechanics

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Citations in the corpus

Off-policy evaluation for slate recommendation (2016, background): “Claim 5 (Boman and Hendrickson [3]) .”
Differential Representations for Mesh Processing (2006, background): “The Laplacian matrix is notoriously ill-conditioned: when we add only one anchor, the largest singular value of L̃ is proportional to the maximal degree in the mesh, while a good estimate for the smallest singular value is one over the product of the maximum topological distance of a vertex from the”
Spectral Sparsification of Graphs (2008, methodology): “roof of Lemma 10.2 uses the following lemma bounding how well a path preconditions an edge. It is an example of a Poincar´e inequality [DS91], and it may be derived from the Rank-One Support Lemma of [BH03], the Congestion-Dilation Lemma of [BGH+06], or the Path Lemma of [ST08b]. We include a proof ”
High-Pass Quantization for Mesh Encoding (2003, unknown): “The small eigenvalue of a basic invertible Lapacian is typically tiny; a good estimate for |λ −1 n | is the product of the maximum topological distance of a vertex from the anchor vertex, and the number of vertices in the mesh (assuming there is one connected component; otherwise the maximum of the ”
Spectral Graph Theory (2012, methodology): “The resulting bounds are called Poincaré inequalities, and are closely related to the bounds used in the analysis of preconditioners in Chapter 12 and in related works [64, 65, 66, 67].”
Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems (2003, methodology): “for every β> 0. Boman and Hendrickson [ 6 , 7] applied the trees of [2] to construct 0-ultra-sparse m 1+o(1) -approximations of A, and showed that these could be used to solve arbitrary SDD systems in time m 1.5+o(1) log(κf (A)/� ). Exploiting”
Nearly-Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems (2006, methodology): “An algebraic extension of Vaidya’s techniques for bounding the condition number was presented by Boman and Hendrickson [BH03b], and later used by them [BH01] to prove that the low-stretch spanning trees constructed by Alon, Karp, Peleg, and West [AKPW95], yield preconditioners for which the precondi”