We propose a modification to Newton’s method for solving nonlinear equations, namely a Jacobian Computation-free Newton’s Method . Unlike the classical Newton’s method, the proposed modification neither requires to compute and store the Jacobian matrix, nor to solve a system of linear equations in each iteration. This is made possible by approximating the Jacobian inverse to a diagonal matrix w...

The objective of this paper is to present and make a comparative study of several inverse kinematics methods for serial manipulators, based on the Jacobian matrix. Besides the well-known Jacobian transpose and Jacobian pseudo-inverse methods, three others, borrowed from numerical analysis, are presented. Among them, two approximation methods avoid the explicit manipulability matrix inversion, w...

MEMS technology exploits the existing microelectronics infrastructure to create complex machines with micron feature sizes. These machines can perform complex functions including communication, actuation and sensing. However, micron sized devices with incompatible processes, different materials, or complex geometries, have to be ‘assembled’. Manual assembly tasks need highly skilled operator to...

An elimination procedure based on Schur complement calculation is proposed for restoring the nonzero elements of a sparse Jacobian matrix. We provide a sparsity usage parameter that can be specified by users to tune the cost of matrix-vector product calculation and the cost of restoration of the nonzero entries. We employ Pascal seeding to compress the Jacobian matrix. Preliminary numerical tes...

This paper proposes a new Levenberg-Marquardt algorithm that is accelerated by adjusting a Jacobian matrix and a quasi-Hessian matrix. The proposed method partitions the Jacobian matrix into block matrices and employs the inverse of a partitioned matrix to find the inverse of the quasi-Hessian matrix. Our method can avoid expensive operations and save memory in calculating the inverse of the qu...

In this paper, we formulate the manipulator Jacobian matrix in a probabilistic framework based on the random matrix theory (RMT). Due to the limited available information on the system fluctuations, the parametric approaches often prove to be inadequate to appropriately characterize the uncertainty. To overcome this difficulty, we develop two RMTbased probabilistic models for the Jacobian matri...

The PolyMAX estimator is used intensively in modal analysis applications nowadays. The main advantages are its speed and the very clear stabilization diagrams it yields. Recently, an algorithm allowing a fast calculation of confidence intervals has been derived for frequency-domain least-squares estimators based on a common-denominator model. In this contribution, the approach is extended to th...

Abstract: This paper presents a performance metric for the manipulability of constrained serial manipulators. The manipulability measure and manipulability ellipsoid are found from the manipulability Jacobian, which is easily found for serial manipulators as the standard Jacobian matrix, or for parallel manipulators as the Jacobian that gives the mapping from the active joint velocities to the ...

In the numerical simulation of inviscid and viscous compressible fluid flow, implicit Newton-Krylov methods are frequently used. A crucial ingredient of Krylov subspace methods is the evaluation of the product of the Jacobian matrix of the spatial operator, e.g., fluxes, and a Krylov vector. In this article we consider a matrix-free implementation of the Jacobian-vector product within the flow ...

Nonlinear least squares (NLS) problems arise in many applications. The common solvers require to compute and store the corresponding Jacobian matrix explicitly, which is too expensive for large problems. In this paper, we propose an effective Jacobian free method especially for large NLS problems because of the novel combination of using automatic differentiation for J(x)v and J (x)v along with...