NDLI: Problems and Techniques (SIREAD Vol. 44 Issue. 3)

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Problems and Techniques (SIREAD Vol. 44 Issue. 3)

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Flaherty, Joe
Copyright Year	2002
Abstract	Our first article of this installment of Problems and Techniques, by Oliker, Li, Husbands, and Biswas, examines the parallel performance of the conjugate gradient and preconditioned (with incomplete factorization) conjugate gradient solution of symmetric, positive definite, linear algebraic systems. Such problems arise in a variety of circumstances, but the authors focus on finite element discretizations of elliptic partial differential equations on unstructured meshes. They explore a variety of complex and interrelated issues such as iterative numerical algorithms, partitioning and ordering strategies, programming paradigms, and computer performance. They conclude with a number of interesting observations involving the interplay between this issues that may, in fact, apply more widely than their application. In our second article, Immanuel Bomze demonstrates unifying relationships between three seemingly different problems: replicator dynamics, describing the frequencies of self-replicating species in population biology; evolutionary game theory, with implications in economics; and quadratic optimization theory. The unifying principles involve regularity conditions, such as strictness of local solutions, hyperbolicity (asymptotic stability) of equilibria, and quasi-strictness conditions for game equilibria. Interestingly, the game problems derive from the Nobel-prize winning work of Nash, Harsanyi, and Selten, so it's certainly topical stuff, at least in Hollywood. Please enjoy these articles.
Starting Page	371
Ending Page	371
Page Count	1
File Format	PDF
ISSN	00361445
DOI	10.1137/SIREAD000044000003000371000001
e-ISSN	10957200
Journal	SIAM Review (SIREAD)
Issue Number	3
Volume Number	44
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-04
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Computational Mathematics

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