Related papers: Solving the octic by iteration in six dimensions
We established a new eighth-order iterative method, consisting of three steps, for solving nonlinear equations. Per iteration the method requires four evaluations (three function evaluations and one evaluation of the first derivative).…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
Recently, Peter Doyle and Curt McMullen devised an iterative solution to the fifth degree polynomial. At the method's core is a rational mapping of the Riemann sphere with the icosahedral symmetry of a general quintic. Moreover, this map…
Recently, Peter Doyle and Curt McMullen devised an iterative solution to the fifth degree polynomial. At the method's core is a rational mapping of the Riemann sphere with the icosahedral symmetry of a general quintic. Moreover, this map…
This paper presents new six solutions for sixth degree polynomial equation in general forms basing on new theorems, where the possibility to calculate the six roots of any sixth degree equation nearly simultaneously. The proposed roots for…
The requirement for solving a polynomial is a means of breaking its symmetry, which in the case of the quintic, is that of the symmetric group S_5. Induced by its five-dimensional linear permutation representation is a three-dimensional…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
A three-point iterative method for solving scalar non-linear equations was selected and then adapted to solve systems of non-linear equations. Subsequently, by applying Taylor's theorem to functions of $\R^{n}$ in $\R^{n}$, it is shown that…
This paper presents iterative methods for solving tensor equations involving the T-product. The proposed approaches apply tensor computations without matrix construction. For each initial tensor, these algorithms solve related problems in a…
In this paper, we study how the D-iteration algorithm can be applied to numerically solve the differential equations such as heat equation in 2D or 3D. The method can be applied on the class of problems that can be addressed by the…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…
This article shows how to find the solution of an arbitrary quintic equation by performing two simultaneous folds on a sheet of paper. The folds achieve specific incidences between a set of points and lines that are determined by the…
A convergent iterative process is constructed for solving any solvable linear equation in a Hilbert space.
In this paper we presents an algorithm for finding a solution of the linear nonhomogeneous quaternionic-valued differential equations. Moveover, several examples shows the feasibility of our algorithm.
In this paper we present a new method of solving certain quartic and higher degree homogeneous polynomial diophantine equations in four variables. The method can also be extended to solve simultaneous homogeneous polynomial diophantine…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
Our paper "Solving Third Order Linear Difference Equations in Terms of Second Order Equations" gave two algorithms for solving difference equations in terms of lower order equations: an algorithm for absolute factorization, and an algorithm…