Triangular systems play a fundamental role in matrix computations. It has been prominently stated in the literature, but is perhaps not widely appreciated, that solutions to triangular systems are usually computed to high accuracy--higher than the traditional condition numbers for linear systems suggest. This phenomenon is investigated by use of condition numbers appropriate to the componentwis...

The main purpose of this paper was to evaluate the performance of the triangular vanes located on the bed and their effect on the bed topography considering different flow conditions. For this purpose, tests were carried out on a straight flume for different flow conditions (five Froude numbers of 0.18, 0.20, 0.22, 0.24 and 0.26) by installing a series of triangular vanes at a space of 4Le (Le ...

This paper considers the problem of computing the Bézier representation for a triangular sub-patch on a triangular Bézier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular Bézier patch. Based on de Casteljau recursions and shifting operators, previous methods express the control points of the triangular sub-pat...

Abstract In this paper, multi-objective optimization (MOO) of Al2O3-water nanofluid flow in microchannel heat sinks (MCHS) with triangular ribs is performed using Computational Fluid Dynamics (CFD) techniques and Non-dominated Sorting Genetic Algorithms (NSGA II). At first, nanofluid flow is solved numerically in various MCHS with triangular ribs using CFD techniques. Finally, the CFD data will...

We discuss theoretical aspects of the self-assembly of triangular tiles, in particular, right triangular tiles and equilateral triangular tiles, and the self-assembly of hexagonal tiles. Contrary to intuition, we show that triangular tile assembly systems and square tile assembly systems cannot be simulated by each other in a non-trivial way. More precisely, there exists a square tile assembly ...

Let %? be a separable Hubert space and !T c 3§(J%f) be an algebra of bounded operators. Say F is triangular if ^ n ^ * is a maximal abelian self-adjoint subalgebra (m.a.s.a.) of 3B{%?) and call this m.a.s.a. the diagonal of J7". A triangular algebra is maximal triangular if it is not properly contained in any triangular algebra. Triangular algebras of operators have been studied for 30 years no...

In this paper, we investigate GPU based parallel triangular solvers systematically. The parallel triangular solvers are fundamental to incomplete LU factorization family preconditioners and algebraic multigrid solvers. We develop a new matrix format suitable for GPU devices. Parallel lower triangular solvers and upper triangular solvers are developed for this new data structure. With these solv...

Various broadband multi-resonator gap-coupled configurations of equilateral triangular microstrip antenna and its compact variation, half equilateral triangular microstrip antenna, are proposed. The broadband proximity fed equilateral triangular microstrip antenna yields bandwidth of more than 650 MHz (~44%), whereas equivalent proximity fed gap-coupled half equilateral triangular microstrip an...

Block lower triangular and block upper triangular matrices are popular preconditioners for nonsymmetric saddle point matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned systems are related. Nonsingular saddle point matrices of the form