Related papers: Munchausen Iteration
We give an algorithm for completing an order-$m$ symmetric low-rank tensor from its multilinear entries in time roughly proportional to the number of tensor entries. We apply our tensor completion algorithm to the problem of learning…
New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematics and uses Max-Plus idempotent semiring. Problem of finding longest increasing sub- sequence is reformulated…
We introduce an efficient way, called Newton algorithm, to study arbitrary ideals in C[[x,y]], using a finite succession of Newton polygons. We codify most of the data of the algorithm in a useful combinatorial object, the Newton tree. For…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
The goal of tensor completion is to fill in missing entries of a partially known tensor (possibly including some noise) under a low-rank constraint. This may be formulated as a least-squares problem. The set of tensors of a given…
Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve…
A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…
Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers…
The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a…
We study linear difference equations with variable coefficients in a ring using a new nonlinear method. In a ring with identity, if the homogeneous part of the linear equation has a solution in the unit group of the ring (i.e., a unitary…
The problem of root mean square approximation of a square integrable function by finite linear combinations of exponential functions is considered. It is subdivided into linear and nonlinear parts. The linear approximation problem is…
We propose a simple iterative (SI) algorithm for the maxcut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the cut…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…
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…
The most efficient known method for solving certain computational problems is to construct an iterated map whose fixed points are by design the problem's solution. Although the origins of this idea go back at least to Newton, the clearest…
We construct two optimal Newton-Secant like iterative methods for solving non-linear equations. The proposed classes have convergence order four and eight and cost only three and four function evaluations per iteration, respectively. These…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…