Related papers: Solving nonlinear systems of equations via spectra…
Spectral residual methods are powerful tools for solving nonlinear systems of equations without derivatives. In a recent paper, it was shown that an acceleration technique based on the Sequential Secant Method can greatly improve its…
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
Newton-type solvers have been extensively employed for solving a variety of nonlinear system of algebraic equations. However, for some complex nonlinear system of algebraic equations, efficiently solving these systems remains a challenging…
Sequential Residual Methods try to solve nonlinear systems of equations $F(x)=0$ by iteratively updating the current approximate solution along a residual-related direction. Therefore, memory requirements are minimal and, consequently,…
For nonlinear equations, the homotopy methods (continuation methods) are popular in engineering fields since their convergence regions are large and they are quite reliable to find a solution. The disadvantage of the classical homotopy…
The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
The iterative problem of solving nonlinear equations is studied. A new Newton like iterative method with adjustable parameters is designed based on the dynamic system theory. In order to avoid the derivative function in the iterative…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
Parameter estimation of nonlinear state-space models from input-output data typically requires solving a highly non-convex optimization problem prone to slow convergence and suboptimal solutions. This work improves the reliability and…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
We apply polynomial approximation methods -- known in the numerical PDEs context as spectral methods -- to approximate the vector-valued function that satisfies a linear system of equations where the matrix and the right hand side depend on…
Spectral methods provide an elegant and efficient way of numerically solving differential equations of all kinds. For smooth problems, truncation error for spectral methods vanishes exponentially in the infinity norm and $L_2$-norm.…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…
Many applications involve partial differential equations which admits nontrivial steady state solutions. The design of schemes which are able to describe correctly these equilibrium states may be challenging for numerical methods, in…
In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…