Algorithms and theory of computation handbook

Algorithms and Theory of Computation Handbook, Second Edition

Iv. Branches of Mathematics Iv.21 Numerical Analysis

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Techniques of the Average Case Analysis of Algorithms

This is an extended version of a book chapter that I wrote for the Handbook on Algorithms and Theon) of Computation (Ed. M. Atallah) in which some probabilistic and analytical techniques of the average case analysis of algorithms are reviewed. By analytical techniques we mean those in which complex analysis plays a primary role. We choose one facet of the theory of algorithms, namely that of al...

Normalized Tenacity and Normalized Toughness of Graphs

In this paper, we introduce the novel parameters indicating Normalized Tenacity ($T_N$) and Normalized Toughness ($t_N$) by a modification on existing Tenacity and Toughness parameters.  Using these new parameters enables the graphs with different orders be comparable with each other regarding their vulnerabilities. These parameters are reviewed and discussed for some special graphs as well.

On Moduli of Rings and Quadrilaterals: Algorithms and Experiments

Moduli of rings and quadrilaterals are frequently applied in geometric function theory, see e.g. the Handbook by Kühnau. Yet their exact values are known only in a few special cases. Previously, the class of planar domains with polygonal boundary has been studied by many authors from the point of view of numerical computation. We present here a new hp-FEM algorithm for the computation of moduli...