Related papers: Annealing approach to root-finding
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
We introduce new multilevel methods for solving large-scale unconstrained optimization problems. Specifically, the philosophy of multilevel methods is applied to Newton-type methods that regularize the Newton sub-problem using second order…
We investigate Newton's method for complex polynomials of arbitrary degree $d$, normalized so that all their roots are in the unit disk. For each degree $d$, we give an explicit set $\mathcal{S}_d$ of $3.33d\log^2 d(1 + o(1))$ points with…
In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as Gauss-Newton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then…
This paper focuses on discussing Newton's method and its hybrid with machine learning for the steady state Navier-Stokes Darcy model discretized by mixed element methods. First, a Newton iterative method is introduced for solving the…
In this paper, based on the homotopy continuation method and the interval Newton method, an efficient algorithm is introduced to isolate the real roots of semi-algebraic system. Tests on some random examples and a variety of problems…
Quasi-Newton methods refer to a class of algorithms at the interface between first and second order methods. They aim to progress as substantially as second order methods per iteration, while maintaining the computational complexity of…
Mixed norms that promote structured sparsity have numerous applications in signal processing and machine learning problems. In this work, we present a new algorithm, based on a Newton root search technique, for computing the projection onto…
Shapelet-based algorithms are widely used for time series classification because of their ease of interpretation, but they are currently outperformed by recent state-of-the-art approaches. We present a new formulation of time series…
A new one-parameter family of iterative method for solving nonlinear equations is constructed and studied. Two variants, both with cubic convergence, are developed, one for finding simple zeros and other for multiple zeros of known…
A general class of Newton algorithms on Gra{\ss}mann and Lagrange-Gra{\ss}mann manifolds is introduced, that depends on an arbitrary pair of local coordinates. Local quadratic convergence of the algorithm is shown under a suitable condition…
We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular…
Newton iteration (NI) is an almost 350 years old recursive formula that approximates a simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) that approximates all the roots simultaneously. In this…
Computing the regularized solution of Bayesian linear inverse problems as well as the corresponding regularization parameter is highly desirable in many applications. This paper proposes a novel iterative method, termed the Projected Newton…
Neutron and X-ray reflectometry are important methods for studying thin multilayer systems. The Parratt method and the method of characteristic matrices, also referred to as transfer matrices, are used for simulation, evaluation of…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
Randomized iterative methods have gained recent interest in machine learning and signal processing for solving large-scale linear systems. One such example is the randomized Douglas-Rachford (RDR) method, which updates the iterate by…
We propose a new globally convergent stochastic second order method. Our starting point is the development of a new Sketched Newton-Raphson (SNR) method for solving large scale nonlinear equations of the form $F(x)=0$ with $F:\mathbb{R}^p…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
This paper presents a modification of Secant method for finding roots of equations that uses three points for iteration instead of just two. The development of the mathematical formula to be used in the iteration process is provided…