Search results for "Jacobi method"

On the zeros of Jacobi polynomials

1994

Beam deconvolution in noisy CMB maps

2003

The subject of this paper is beam deconvolution in small angular scale CMB experiments. The beam effect is reversed using the Jacobi iterative method, which was designed to solved systems of algebraic linear equations. The beam is a non circular one which moves according to the observational strategy. A certain realistic level of Gaussian instrumental noise is assumed. The method applies to small scale CMB experiments in general (cases A and B), but we have put particular attention on Planck mission at 100 GHz (cases C and D). In cases B and D, where noise is present, deconvolution allows to correct the main beam distortion effect and recover the initial angular power spectrum up to the end…

Tool-Point Control for a Redundant Heave Compensated Hydraulic Manipulator

2012

Abstract In this paper, theoretical and experimental implementation of heave compensation on a redundant hydraulically actuated manipulator with 3-dof has been carried out. The redundancy is solved using the pseudo-inverse Jacobian method. Techniques for minimizing velocities and avoiding mechanical joint saturations is implemented in the null space joint motion. Model based feed-forward, combined with a PI-controller handles the velocity control of each joint. A time domain simulation model has been developed, experimentally verified, and used for controller parameter tuning. Model verification and experimental results are obtained while the manipulator is exposed to wave disturbances crea…

On the equivalence between the Scheduled Relaxation Jacobi method and Richardson's non-stationary method

2017

The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations ($Au=b$) associated with elliptic problems. It inherits its robustness and accelerates its convergence rate computing a set of $P$ relaxation factors that result from a minimization problem. In a typical SRJ scheme, the former set of factors is employed in cycles of $M$ consecutive iterations until a prescribed tolerance is reached. We present the analytic form for the optimal set of relaxation factors for the case in which all of them are different, and find that the resulting algorithm is equivalent to a non-stationary generalized Richardson's method. …

Scheduled Relaxation Jacobi method: improvements and applications

2016

Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficien…

Jacobi Fields, Conjugate Points

2001

Let us go back to the action principle as realized by Jacobi, i.e., time is eliminated, so we are dealing with the space trajectory of a particle. In particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space.