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Iterative Methods for Linear and Nonlinear Equations

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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.

Comments and Ratings (6)

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.

Shunping Yan

pinkie li

maun budiyanto

It is very simple, so need axpand of material.

Zhonghua Liang

Ciro Raia

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