A Method Of Solving Nonlinear Simultaneous Equations Without Using Jacobian
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A Method of Solving Nonlinear Simultaneous Equations Without Using Jacobian
In this thesis some methods for solving systems of nonlinear equations are described, which do not require calculation of the Jacobian matrix. One of these methods is programmed to solve a parametrized system with possible singularities. The efficiency of this method and a modified Newton's method are compared using experimental results from six test cases.
Solving Nonlinear Equations with Newton's Method
This book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.
A Robust and Efficient Method for Solving Nonlinear Rational Expectations Models
Author: Mr.Douglas Laxton
language: en
Publisher: International Monetary Fund
Release Date: 1996-09-01
The development and use of forward-looking macro models in policymaking institutions has proceeded at a pace much slower than predicted in the early 1980s. An important reason is that researchers have not had access to robust and efficient solution techniques for solving nonlinear forward-looking models. This paper discusses the properties of a new algorithm that is used for solving MULTIMOD, the IMF’s multicountry model of the world economy. This algorithm is considerably faster and much less prone to simulation failures than to traditional algorithms and can also be used to solve individual country models of the same size.