Related papers: Root finding techniques that work
The Semi-Implicit Root solver (SIR) is an iterative method for globally convergent solution of systems of nonlinear equations. Since publication, SIR has proven robustness for a great variety of problems. We here present MATLAB and MAPLE…
We consider multidimensional optimization problems, which are formulated and solved in terms of tropical mathematics. The problems are to minimize (maximize) a linear or nonlinear function defined on vectors over an idempotent semifield,…
Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…
Root cause analysis of anomalies aims to identify how and why a sample deviates from the normal process. Existing methods primarily focus on telling which features are responsible, ignoring that anomalies can arise through two fundamentally…
We describe a method for calculating the roots of special functions satisfying second order linear ordinary differential equations. It exploits the recent observation that the solutions of a large class of such equations can be represented…
The aim of this paper is to introduce a new Newton-type iterative method and then to show that this process converges to the unique solution of the scalar nonlinear equation f(x)=0 under weaker conditions involving only f and f' by fixed…
A new problem is studied, the concept of exactness of a second order nonlinear ordinary differential equations is established. A method is constructed to reduce this class into a first order equations. If the second order equation is not…
The textbook Newton's iteration is practically inapplicable on solutions of nonlinear systems with singular Jacobians. By a simple modification, a novel extension of Newton's iteration regains its local quadratic convergence toward…
In this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown.…
This article demonstrates how variation of parameters can be successfully implemented in combination with other classical techniques, such as the method of characteristics, to derive novel classes of solutions to nonlinear partial…
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…
Non-trivial analysis problems require posets with infinite ascending and descending chains. In order to compute reasonably precise post-fixpoints of the resulting systems of equations, Cousot and Cousot have suggested accelerated fixpoint…
Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
The intention of the present study is to establish the mathematical fundamentals for automated problem solving essentially targeted for robotics by approaching the task universal algebraically introducing knowledge as realizations of…
We shall study special regularity properties of solutions to some nonlinear dispersive models. The goal is to show how regularity on the initial data is transferred to the solutions. This will depend on the spaces where regularity is…
Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a very difficult problem with many applications. While it is hopeless to expect much in general, we know a surprising amount about these…
In this article we present logarithmic methods for solving first order and second order ordinary differential equations. The essence of the method is that we apply the basic properties derivatives and logarithms to reduce the number of…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
In this paper, we propose some algorithms for analytical solution construction to nonlinear polynomial partial differential equations with constant function coefficients. These schemes are based on one-(single), two- (double) or three-…