An approach for solving sparse triangular systems of equations on highly parallel computers employs a partitioned representation of the inverse of the triangular matrix so that the solution can be obtained by a series of matrix-vector multiplications. This approach requires a number of global communication steps that is proportional to the number of factors in the partitioning. The problem of n...

We are interested in the design of efficient geometric multigrid methods on hierarchical triangular grids for problems in two dimensions. Fourier analysis is a well-known useful tool in multigrid for the prediction of two-grid convergence rates which has been used mainly for rectangular–grids. This analysis can be extended straightforwardly to triangular grids by using an appropriate expression...

Let F be a field and m,n be integers m,n > 3. Let SMn(F) and STn(F) denote the linear space of n × n per-symmetric matrices over F and the linear space of n × n per-symmetric triangular matrices over F, respectively. In this note, the structure of spaces of bounded rank-two matrices of STn(F) is determined. Using this structural result, a classification of bounded rank-two linear preservers ψ :...

We propose a method based on Cholesky decomposition for Non-negative Matrix Factorization (NMF). NMF enables to learn local representation due to its non-negative constraint. However, when utilizing NMF as a representation leaning method, the issues due to the non-orthogonality of the learned representation has not been dealt with. Since NMF learns both feature vectors and data vectors in the f...

The popularity of Partitioned Global Address Space (PGAS) languages has increased during the last years thanks to their high programmability and performance through an efficient exploitation of data locality. This paper describes the implementation of efficient parallel dense triangular solvers in the PGAS language Unified Parallel C (UPC). The solvers are built on top of sequential BLAS functi...

We focus on the behavior of solutions of the difference equation xn b1xn−1 b2xn−2 · · · bnx0 yn, n 1, 2, . . ., where bk is a fixed sequence of complex numbers, and yk is a fixed sequence in a complex Banach space. We give the general solution of this difference equation. To examine the asymptotic behavior of solutions, we compute the spectra of operators which correspond to such type of differ...

Abstract In this paper we explain the fractal geometry of refined and derefined triangular and tetrahedral meshes by means of the application of iterated function systems (IFS). These meshes feature a remarkable amplifying invariance under changes of scale. The applications of IFS families are shown equivalent to the use of adaptive strategies that combine the refinement procedure with the dere...

In this paper we develop a novel image processing technique to register two dimensional temporal mammograms for effective diagnosis and therapy. Our registration framework is founded upon triangular B-spline finite element method (TBFEM). In contrast to tensor-product B-splines, which is widely used in medical imaging, triangular B-splines are much more powerful, associated with many desirable ...

The two dimensional Euler equations have been solved on a regular triangular grid using the finite volume approach. By careful construction of the dissipative terms, the scheme is designed to be second order accurate in space, provided the grid is smooth, except in the vicinity of shocks, where it behaves as first order accurate. The multigrid technique has been applled to triangular meshes to ...

Quantum chaotic states over a noncommutative monoid, a unitalization of a noncommutative Ito algebra parametrizing a quantum stochastic Levy process, are described in terms of their infinitely divisible generating functionals over the simple monoid-valued fields on an atomless ‘space-time’ set. A canonical decomposition of the logarithmic conditionally posive-definite generating functional is c...