Displaying similar documents to “Dual cones and the Voronoi algorithm.”

Conjugate gradient algorithms for conic functions

Ladislav Lukšan (1986)

Aplikace matematiky

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The paper contains a description and an analysis of two modifications of the conjugate gradient method for unconstrained minimization which find a minimum of the conic function after a finite number of steps. Moreover, further extension of the conjugate gradient method is given which is based on a more general class of the model functions.

Cyclotomic quadratic forms

François Sigrist (2000)

Journal de théorie des nombres de Bordeaux

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Voronoï ’s algorithm is a method for obtaining the complete list of perfect n -dimensional quadratic forms. Its generalization to G -forms has the advantage of running in a lower-dimensional space, and furnishes a finite, and complete, classification of G -perfect forms ( G is a finite subgroup of G L ( n , ℤ ) ) . We study the standard, φ ( m ) -dimensional irreducible representation of the cyclic group C m of order m , and give the, often new, densest G -forms. Perfect cyclotomic forms are completely classified...

Linking the closure and orthogonality properties of perfect morphisms in a category

David Holgate (1998)

Commentationes Mathematicae Universitatis Carolinae

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We define perfect morphisms to be those which are the pullback of their image under a given endofunctor. The interplay of these morphisms with other generalisations of perfect maps is investigated. In particular, closure operator theory is used to link closure and orthogonality properties of such morphisms. A number of detailed examples are given.