Among offshore hydrocarbon exploration technologies, the controlled source electromagnetic (CSEM) method have gained a lot of interest in both academia and industry because of its ability to detect hydrocarbon reservoirs [1]. In order to maximally extract information from the data, a full nonlinear inversion approach is employed [2]. In such an approach, the investigation domain is subdivided i...

Estimating the Jacobian matrix of a nonlinear dynamical system through observed time-series data is one of the important steps in predicting future states of the time series. The Jacobian matrix is estimated using local information about divergences of nearby trajectories. Although the basic algorithm for estimating the Jacobian matrix generally works well, it often fails for short or noisy dat...

This work presents a re-derivation of relative Jacobian matrix for parallel manipulators, expressed in terms of the individual manipulator Jacobians and multiplied by their corresponding transformation matrices. This is particularly useful when the individual manipulator Jacobians are given, such that one would not need to derive an entirely new expression of a relative Jacobian but will only u...

The instantaneous kinematic analysis of a manipulator defines the direction and magnitude (translational and rotational) of impending motion at a specific point in time. This analysis is position dependent, and assumes apriori knowledge of the position information. From the position kinematic analysis, a kinematic transformation between joint space and tool space can be represented as: ( ) x = ...

By using the Hadamard matrix product concept, this paper introduces two generalized matrix formulation forms of numerical analogue of nonlinear differential operators. The SJT matrix-vector product approach is found to be a simple, efficient and accurate technique in the calculation of the Jacobian matrix of the nonlinear discretization by finite difference, finite volume, collocation, dual rec...

In this paper, we propose a versatile visual servo-ing control scheme with a Jacobian matrix estimator. The Jacobian matrix estimator does not need a priori knowledge of the kinematic structure and parameters of the robot system, such as camera and link parameters. The proposed visual servoing control scheme ensures the convergence of the image-features to desired trajectories, by using the est...

According to the principle of transference, a compact three-dimensional representation of a rigid body kinematics is obtained by substituting dual for real numbers. This representation has recently been applied to robotics where in addition to its compactness, it allows to constitute the Jacobian matrix explicitly from the product of the dual transformation matrices with no additional computati...

Our aim is to stress the importance of Jacobian matrix conditioning for model validation. We also comment on Monari and Dreyfus (2002), where, following Rivals and Personnaz (2000), it is proposed to discard neural candidates that are likely to overfit and/or for which quantities of interest such as confidence intervals cannot be computed accurately. In Rivals and Personnaz (2000), we argued th...

The error backpropagation (EBP) algorithm for training feedforward multilayer perceptron (FMLP) has been used in many applications because it is simple and easy to implement. However, its gradient descent method prevents EBP algorithm from converging fast. To overcome the slow convergence of EBP algorithm, the second order methods have adapted. Levenberg-Marquardt (LM) algorithm is estimated to...

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...