A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations
نویسندگان
چکیده
We propose an approach to enhance the performance of a diagonal variant of secant method for solving large-scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to improve the updated approximate Jacobian in diagonal form. The numerical results verify that the proposed approach is a clear enhancement in numerical performance.
منابع مشابه
An Implicit Multi-Step Diagonal Secant-Type Method for Solving Large-Scale Systems of Nonlinear Equations
This paper presents an improved diagonal Secant-like method using two-step approach for solving large scale systems of nonlinear equations. In this scheme, instead of using direct updating matrix in every iteration to construct the interpolation curves, we chose to use an implicit updating approach to obtain an enhanced approximation of the Jacobian matrix which only requires a vector storage. ...
متن کاملA Three-terms Conjugate Gradient Algorithm for Solving Large-Scale Systems of Nonlinear Equations
Nonlinear conjugate gradient method is well known in solving large-scale unconstrained optimization problems due to it’s low storage requirement and simple to implement. Research activities on it’s application to handle higher dimensional systems of nonlinear equations are just beginning. This paper presents a Threeterm Conjugate Gradient algorithm for solving Large-Scale systems of nonlinear e...
متن کاملA matrix-free quasi-Newton method for solving large-scale nonlinear systems
One of the widely used methods for solving a nonlinear system of equations is the quasi-Newton method. The basic idea underlining this type of method is to approximate the solution of Newton's equation by means of approximating the Jacobian matrix via quasi-Newton update. Application of quasi-Newton methods for large scale problems requires, in principle, vast computational resource to form and...
متن کاملAn Enhanced Matrix-Free Secant Method via Predictor-Corrector Modified Line Search Strategies for Solving Systems of Nonlinear Equations
Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our a...
متن کاملA NEW TWO STEP CLASS OF METHODS WITH MEMORY FOR SOLVING NONLINEAR EQUATIONS WITH HIGH EFFICIENCY INDEX
It is attempted to extend a two-step without memory method to it's with memory. Then, a new two-step derivative free class of without memory methods, requiring three function evaluations per step, is suggested by using a convenient weight function for solving nonlinear equations. Eventually, we obtain a new class of methods by employing a self-accelerating parameter calculated in each iterative...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Applied Mathematics
دوره 2012 شماره
صفحات -
تاریخ انتشار 2012