Rational functions, Toda flows, and LR-like algorithms

Scaled Toda like Flows

This paper discusses the class of isospectral ows X X A X where denotes the Hadamard product and is the Lie bracket The presence of A allows arbitrary and independent scaling for each element in the matrix X The time mapping of the scaled Toda like ow still enjoys a QR like iteration The scaled structure includes the classical Toda ow Brockett s double bracket ow and other interesting ows as sp...

Generalised LR parsing algorithms

This thesis concerns the parsing of context-free grammars. A parser is a tool, defined for a specific grammar, that constructs a syntactic representation of an input string and determines if the string is grammatically correct or not. An algorithm that is capable of parsing any context-free grammar is called a generalised (contextfree) parser. This thesis is devoted to the theoretical analysis ...

Algorithms for Indeenite Summation of Rational Functions in Maple Algorithms for Indeenite Summation of Rational Functions in Maple

Probability, Networks and Algorithms Probability, Networks and Algorithms Global optimization of rational multivariate functions

The paper deals with unconstrained global minimization of rational functions. A necessary condition is given for the function to have a nite in mum. In case the condition is satis ed, the problem is shown to be equivalent to a speci c constrained polynomial optimization problem. In this paper, we solve a relaxation of the latter formulation using semi-de nite programming. In general, the relaxa...

Wall rational functions and Khrushchev’s formula for orthogonal rational functions

We prove that the Nevalinna-Pick algorithm provides different homeomorphisms between certain topological spaces of measures, analytic functions and sequences of complex numbers. This algorithm also yields a continued fraction expansion of every Schur function, whose approximants are identified. The approximants are quotients of rational functions which can be understood as the rational analogs ...