Related papers: Factored solution of nonlinear equation systems
A general solution is found for a large class of time continuous autonomous nonlinear dynamical systems, the so-called quasi-polynomial systems. This solution is expressed in terms of a new type of special functions defined via their Taylor…
When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this…
A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.
A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE's contains…
Non-negative Matrix Factorization (NMF) asks to decompose a (entry-wise) non-negative matrix into the product of two smaller-sized nonnegative matrices, which has been shown intractable in general. In order to overcome this issue, the…
We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…
A modification of Newton's method for solving systems of $n$ nonlinear equations is presented. The new matrix-free method relies on a given decomposition of the invertible Jacobian of the residual into invertible sparse local Jacobians…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
The numerical solution of problems in nonlinear magnetostatics is typically based on a variational formulation in terms of magnetic potentials, the discretization by finite elements, and iterative solvers like the Newton method. The vector…
Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first…
Single scale Feynman integrals in quantum field theories obey difference or differential equations with respect to their discrete parameter $N$ or continuous parameter $x$. The analysis of these equations reveals to which order they…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
We present a family of fast and accurate Dijkstra-like solvers for the eikonal equation and factored eikonal equation which compute solutions on a regular grid by solving local variational minimization problems. Our methods converge…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
This paper proposes the design and implementation strategy of a novel computing architecture, the Factor Machine. The work is a step towards a general-purpose parallel system operating in a non-sequential manner, exploiting…