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### Highlights from Iterative Methods for Linear and Nonlinear Equations

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# Iterative Methods for Linear and Nonlinear Equations

### C.T. Kelley (view profile)

21 Aug 2002 (Updated )

Companion Software

File Information
Description

This book provides a complete analysis of the conjugate gradient and generalized minimum residual iterations.
For a full book description and ordering information, please refer to http://www.mathworks.com/support/books/book1344.jsp.

MATLAB release MATLAB 5.2 (R10)
MATLAB Search Path
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02 Jul 2016 A S

### A S (view profile)

Came here to learn about some advanced methods for nonlinear equation solving.

1. multiple solvers did not work out of the box because of some trivial programming errors, like output arguments not set. No big deal.

2. The actual problem however seems to be that... well, actually most solvers fail for even the simplest problems. See the following code:

fun1 = @(x) -2 + x.^2;
x0 = 5;

%% newton solver:
[sol, it_hist, ierr] = nsol(x0,fun1,[1e-3, 1e-3],[40, 1, 0]);
sol

%% globalized newton solver
[sol, it_hist, ierr] = nsola(x0,fun1,[1e-3, 1e-3],[40, 40, 0.9, 1, 20]);
sol

%% Newton-GMRES locally convergent solver for f(x) = 0
[sol, it_hist, ierr] = nsolgm(x0,fun1,[1e-3, 1e-3],[40, 40, 0.9]);
sol

%% Broyden's Method solver, globally convergent
[sol, it_hist, ierr] = brsola(x0,fun1,[1e-3, 1e-3],[40, 40]);
sol

%% Broyden's Method solver, locally convergent
[sol, it_hist, ierr] = brsol(x0,fun1,[1e-3, 1e-3],[40, 40, 0]);
sol

Here, only the classical newton solver will succeed. Even for a purely convex function as used here. There is absolutely no difficulty in getting the zero of a parabola.

Comment only
26 Mar 2016 Shunping Yan

### Shunping Yan (view profile)

29 Nov 2015 pinkie li

### pinkie li (view profile)

29 Nov 2005 maun budiyanto

It is very simple, so need axpand of material.

25 Nov 2005 Zhonghua Liang
09 Jul 2003 Ciro Raia