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Lattice rules of minimal and maximal rank with good figures of merit

✍ Scribed by T.N. Langtry

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 143 KB
Volume: 112
Category: Article
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(99)00220-4

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✦ Synopsis

For periodic integrands with unit period in each variable, certain error bounds for lattice rules are conveniently characterised by the ÿgure of merit , which was originally introduced in the context of number theoretic rules. The problem of ÿnding good rules of order N (that is, having N distinct nodes) then becomes that of ÿnding rules with large values of . This paper presents e cient search methods for the discovery of rank 1 rules, and of maximal rank rules of high order, which possess good ÿgures of merit.

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Maximization and minimization of the rank and inertia of the Hermitian matrix expression with applications

✍ Yongge Tian 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 465 KB

We give in this paper a group of closed-form formulas for the maximal and minimal ranks and inertias of the linear Hermitian matrix function A -BX -(BX) \* with respect to a variable matrix X. As applications, we derive the extremal ranks and inertias of the matrices X ±X \* , where X is a solution