We present a recursive way to partition hypergraphs which creates and exploits hypergraph geometry and is suitable for many-core parallel architectures. Such partitionings are then used to bring sparse matrices in a recursive Bordered Block Diagonal form (for processor-oblivious parallel LU decomposition) or recursive Separated Block Diagonal form (for cache-oblivious sparse matrix–vector multi...

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Over the last two decades a considerable amount of e ort has been put in the development and applica tion of matrix geometric techniques for the analysis of queueing systems of which the embedded Markov chain exhibits a regular structure Most of this work however has been presented in either a mathematical context or in a purely application oriented context In this paper we present Xmgm a perfo...

Considered is a linear set of ordinary differential equations with a matrix depending on a set of adiabatically varying parameters. Asymptotic solutions have been constructed. As has been shown, an important characteristic determining the qualitative portrait of the system is the real part of Berry’s complex geometric phase, which we call the geometric amplitude. For systems with purely imagina...

A new method is presented to study the interaction of multiple cracks, especially for areas near crack tips by using extended finite element method. In order track a geometric tracking technique proposed enriched elements and nodes along instead narrow band level set This allows accurately determine calculate enrichment values. constructing multicrack matrix, which involves numbering cracks sol...

The research of geometric means of matrices is attracting more and more attention from scholars since it has very important applications in mathematics and physics, especially in the von Neuman entropy involving the quantum physics and statistical thermal physical. There are many achievements on the entropy, among which the entropy uncertainty relation, the generalization of the Heisenberg unce...

In 1969, V. Strassen improves the classical~2x2 matrix multiplication algorithm. The current upper bound for 3x3 matrix multiplication was reached by J.B. Laderman in 1976. This note presents a geometric relationship between Strassen and Laderman algorithms. By doing so, we retrieve a geometric formulation of results very similar to those presented by O. Sykora in 1977.

Ž . For photogrammetric applications, solutions to camera exterior orientation problem can be classified into linear direct and non-linear. Direct solutions are important because of their computational efficiency. Existing linear solutions suffer from lack of robustness and accuracy partially due to the fact that the majority of the methods utilize only one type of geometric entity and their fr...