interval of convergence

interval of convergence

[′in·tər·vəl əv kən′vər·jəns]
(mathematics)
The interval consisting of the real numbers for which a specified power series possesses a limit.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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function [sol, nr_it] = bisection_method(f, a, b, eps) % f is a continuous function, whose root is being approximated; % [a,b} is the interval on which a root exists and f(a)f(b)<0; % eps is the specified error for the approximation; % if no eps is specified, % the default will be 10^(-5); % sol is the approximation of the solution; % nr_it is the number of iterations needed for tolerance err; if nargin < 4 eps=1e-5; end n=0; x = (a + b)/2; while b - a >= eps n = n + 1; x = (a + b)/2; if f(a)*f(x) < 0 b = x; else a = x; end end sol = x; nr_it = n; end Since the next three methods do not converge for all initial values, we introduce a maximum number of iterations allowed, in case the initial values are not within the interval of convergence.
These results are obtained for different values of h laying in the interval of convergence.