This paper studies the performance of different algorithms for solving a dense symmetric indefinite linear system of equations on multicore CPUs with a Graphics Processing Unit (GPU). To ensure the numerical stability of the factorization, pivoting is required. Obtaining high performance of such algorithms on the GPU is difficult because all the existing pivoting strategies lead to frequent syn...

Combinatorial optimization problems on graphs arise in many practical applications. One of the most studied practical combinatorial optimization problem is the Vehicle Routing Problem (VRP). When coupled with modern in-car navigation and fleet management software, real world applications of VRP optimization result in significant cost savings. In this paper novel multiple improvements pivoting r...

Recognizing and generating paraphrases is an important component in many natural language processing applications. A wellestablished technique for automatically extracting paraphrases leverages bilingual corpora to find meaning-equivalent phrases in a single language by “pivoting” over a shared translation in another language. In this paper we revisit bilingual pivoting in the context of neural...

Developing country food supply chains have been pummeled by a series (and often confluence) of shocks over the past several decades, including Russia-Ukraine war, COVID-19, climate from hurricanes to floods droughts, animal and plant diseases, an intensification road banditry local conflicts, overlaying all these, deep transformation in markets themselves with new requirements for quality safet...

An algorithm for the solution of banded linear systems is presented and discussed which combines stability with scalability. This is achieved by implementing divide and conquer for Gaussian elimination with partial pivoting. Earlier divide and conquer algorithms for Gaussian elimination have problems with instabil-ities and can even break down as they implement a more restricted form of pivotin...

We consider the direct solution of sparse symmetric indefinite matrices. We develop new pivoting strategies that combine numerical and static pivoting. Furthermore, we propose original approaches that are designed for parallel distributed factorization. We show that our pivoting strategies are numerically robust and that the factorization is significantly faster because of this static/numerical...

In this paper we address whole-body manipulation of bulky objects by a humanoid robot. We adopt a “pivoting” manipulation method that allows the humanoid to displace an object without lifting, but by the support of the ground contact. First, the smalltime controllability of pivoting is demonstrated. On its basis, an algorithm for collision-free pivoting motion planning is established taking int...

Many standard matrix algorithms are diicult to implement as systolic arrays, because they involve data movement that cannot be determined a priori, resulting in high timing complexity. In the case of dense matrix inversion, Gaussian elimination (GE) with pivoting has largely been supplanted by alternative schemes, such as Givens rotations and the Gram-Schmidt method, which are costly and comple...

This paper presents “oriented pivoting systems” as an abstract framework for complementary pivoting. It gives a unified simple proof that the endpoints of complementary pivoting paths have opposite sign. A special case are the Nash equilibria of a bimatrix game at the ends of Lemke–Howson paths, which have opposite index. For Euler complexes or “oiks”, an orientation is defined which extends th...

In this paper, we investigate the planar dynamic pivoting problem, in which a pinched object is reoriented to a desired pose through wrist swing motion and grip force regulation. Traditional approaches based on friction compensation do not work well for this problem, as we observe the torsional friction at the contact has large uncertainties during pivoting. In addition, the discontinuities of ...