Simulations and optimizations are carried out to investigate real-world problems in science and engineering. For instance, solving systems of linear equations with sparse Jacobian matrices is mandatory when using a Newton-type algorithm. The sparsity of Jacobian matrices is exploited and only a subset of the nonzero elements is determined to successfully reduce the usage of the restricting reso...

We have combined inverse kinematics learned by LWPR with visual servoing to correct for inaccuracies in a low cost robotic arm. By low cost we mean weak inaccurate servos and no available joint-feedback. We show that from the trained LWPR model the Jacobian can be estimated. The Jacobian maps wanted changes in position to corresponding changes in control signals. Estimating the Jacobian for the...

The sine-Gordon equation has hyperelliptic al function solutions over a hyperelliptic Jacobian for y = f(x) of arbitrary genus g. This article gives an extension of the sine-Gordon equation to that over subvarieties of the hyperelliptic Jacobian. We also obtain the condition that the sine-Gordon equation in a proper subvariety of the Jacobian is defined.

Any endomorphism of Cn defined by n polynomials with everywhere non-vanishing Jacobian is an automorphism. The Jacobian conjecture originated fromKeller ([5]). Let F1, . . . , Fn ∈ C[x1, . . . , xn] be a set of n polynomials in n variables with n ≥ 1 such that the Jacobian of these polynomials is a nonzero constant. The Jacobian conjecture says that the subalgebra C[F1, . . . , Fn] of C[x1, . ....

Consider the Jacobian of a genus two curve defined over a finite field and with complex multiplication. In this paper we show that if the l-Sylow subgroup of the Jacobian is not cyclic, then the embedding degree of the Jacobian with respect to l is one.

Newton-Krylov methods, combination of Newton-like methods and Krylov subspace methods for solving the Newton equations, often need adequate preconditioning in order to be successful. Approximations of the Jacobian matrices are required to form preconditioners and this step is very often the dominant cost of Newton-Krylov methods. Therefore, working with preconditioners destroys in principle the...

A parametric, continuous-time Markov model for digraph panel data is considered. The parameter is estimated by the method of moments. A convenient method for estimating the variance–covariance matrix of the moment estimator relies on the delta method, requiring the Jacobian matrix—that is, the matrix of partial derivatives—of the estimating function. The Jacobian matrix was estimated hitherto b...

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...

Counting the order of the Jacobian group of a hyperelliptic curve over a nite eld is very important for constructing a hyperelliptic curve cryptosystem (HECC), but known algorithms to compute the order of a Jacobian group over a given large prime eld need very long running times. In this note, we propose a practical polynomial-time algorithm to compute the order of the Jacobian group for a hype...

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...