We show that an interior-point method for monotone variational inequalities exhibits superlinear convergence provided that all the standard assumptions hold except for the well-known assumption that the Jacobian of the active constraints has full rank at the solution. We show that superlinear convergence occurs even when the constant-rank condition on the Jacobian assumed in an earlier work doe...

For redundant manipulators, the inverse kinematics equations are typically solved by taking the pseudoinverse of the Jacobian, or by adding enough constraints to algebraically remove the redundancy. Many popular measures of redundancy also depend on computing the algebraic rank or determinant of the Jacobian. We present fast, parallelizable algorithms to dynamically update all the pseudo-invers...

We classify all polynomial maps of the form [Formula: see text] in case when Jacobian matrix is nilpotent and highest degree no more than 1. In addition, we generalize structure to text].

Determining all rational points on a curve of genus at least 2 can be difficult. Chabauty's method (1941) is to intersect, for prime number p, in the p-adic Lie group jacobian, closure Mordell-Weil with curve. If rank less than then this has never failed. Minhyong Kim's non-abelian Chabauty programme aims remove condition rank. The simplest case, called quadratic Chabauty, was developed by Bala...

This paper presents a novel approach to compute the rank-deficiency locus of non-square Jacobian matrices. This algorithm is based on the computation of the singular vectors associated to zero singular values of the Jacobian. Examples are provided to illustrate the application of the algorithm. Results are shown for a four degree-of-freedom and a seven degree-of-freedom manipulator.

A central problem in Diophantine geometry is to uniformly bound the number of $K$-rational points on a smooth curve $X/K$ terms $K$ and its genus $g$. recent paper by Stoll proved uniform bounds for hyperelliptic $X$ provided that rank Jacobian at most $g - 3$. Katz, Rabinoff Zureick-Brown generalized his result arbitrary curves satisfying same condition. In this paper, we prove conditional r...

The articulated arm coordinate measuring machine (AACMM) is a kind of new coordinate measuring device based on non-Cartesian system. The measuring accuracy of the AACMM can be effectively improved by parameter identification. However, some of the structural parameters are coupling (linearly related), so the structural parameters usually cannot be identified correctly. The Jacobian matrix was ob...