Based on the generalized Gauss±Newton method, a new algorithm to minimize the objective function of the penalty method in (Bentley LR. Adv Wat Res 1993;14:137±48) for inverse problems of steady-state aquifer models is proposed. Through detailed analysis of the ``built-in'' but irregular weighting e€ects of the coecient matrix on the residuals on the discrete governing equations, a so-called sc...

The Newton-Schulz iteration is a quadratically convergent, inversion-free method for computing the sign function of a matrix. It is advantageous over other methods for high-performance computing because it is rich in matrix-matrix multiplications. In this paper we propose a variant for Hermitian matrices that improves the initially slow convergence of the iteration. The main idea is to scale th...

The solution to the problem of factorization of the covariance function of a stationary, discrete-time process is obtained by using a Newton-Raphson procedure which converges quadratically in I1 provided the initial iterate is chosen suitably. The existence of a suitable initial iterate is guaranteed by an approximation result. An application to error localization in spectral factorization is s...

The solution of an integral equation arising in a covariance factorization problem is obtained by a Newton-Raphson iteration that is almost always globally convergent. Interpretations of the iterates are given, and the result is shown to specialize to known algorithms when the covariance is stationary with a rational Fourier transform.

Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness in the ordinary Newton method of suffering a high cost at each iteration while commanding a high convergence rate. In this work we propose two new efficient ...

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...

A new registration algorithm based on Newton-Raphson iteration is proposed to align images with rigid body transformation. A set of transformation parameters consisting of translation in x and y and rotation angle around z is calculated by optimizing a specified similarity metric using the Newton-Raphson method. This algorithm has been tested by registering and correlating pairs of topography m...

We consider the simulation of three-dimensional transonic Euler flow using pseudo-transient Newton–Krylov methods [8,9]. The main computation involves solving a large, sparse linear system at each Newton (nonlinear) iteration. We develop a technique for adaptively selecting the linear solver method to match better the numeric properties of the linear systems as they evolve during the course of ...

The smoothness-constrained least-squares method is widely used for two-dimensional (2D) and three-dimensional (3D) inversion of apparent resistivity data sets. The Gauss–Newton method that recalculates the Jacobian matrix of partial derivatives for all iterations is commonly used to solve the least-squares equation. The quasi-Newton method has also been used to reduce the computer time. In this...

In recent years, there has been an increasing interest in developing new algorithms for digital signal processing by applying and generalising existing numerical linear algebra tools. A recent result shows that the FastICA algorithm, a popular state-of-the-art method for linear Independent Component Analysis (ICA), shares a nice interpretation as a Newton type method with the Rayleigh Quotient ...