11-Using-fzero-and-Applications-4UP

# 11-Using-fzero-and-Applications-4UP - fzero Nonlinear...

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Unformatted text preview: fzero Nonlinear problems with parameters More on Newton Using fzero and Applications Dhavide Aruliah UOIT MATH 2072U c D. Aruliah (UOIT) Using fzero and Applications MATH 2072U 1 / 23 fzero Nonlinear problems with parameters More on Newton Using fzero and Applications 1 Using MATLAB’s fzero 2 Solving nonlinear equations with parameters 3 More on Newton-based algorithms c D. Aruliah (UOIT) Using fzero and Applications MATH 2072U 2 / 23 fzero Nonlinear problems with parameters More on Newton fzero MATLAB has practical zero-finding routine fzero Can specify initial interval I ( ) = [ a ( ) , b ( ) ] bracketing zero f = @(x) x-cos(x) % Function to find zeros I0 = [0.5, 1.0]; % Initial interval x = fzero( f, I0 ) Alternatively, fzero accepts a single value x ( ) as initial iterate f = @(x) x-cos(x) % Function to find zeros x0 = 1.0; % Initial iterate x = fzero( f, x0 ) c D. Aruliah (UOIT) Using fzero and Applications MATH 2072U 4 / 23 fzero Nonlinear problems with parameters More on Newton fzerogui : Illustration of algorithm for fzero Graphical interface to fzero Can select iterates with mouse Iterates generated from either I bisection method I secant method I inverse quadratic interpolation (IQI) Some examples to try: I x 3- 2 x- 5 on [ 0, 3 ] I ln ( x + 2/3 ) on [ 0, 1 ] c D. Aruliah (UOIT) Using fzero and Applications MATH 2072U 5 / 23 fzero Nonlinear problems with parameters More on Newton Syntax for fzero x = fzero(fun,x0) x = fzero(fun,x0,options) [x,fval] = fzero(...) [x,fval,exitflag] = fzero(...) [x,fval,exitflag,output] = fzero(...) options is a structure whose fields can specify, display preferences, tolerances, maximum number of iterations, etc. fzero is a function function : expects function handle fun as input c D. Aruliah (UOIT) Using fzero and Applications MATH 2072U 6 / 23 fzero Nonlinear problems with parameters More on Newton Nonlinear functions with parameters Parametrised families of nonlinear equations are common e.g., α sin x + β e- x 2 /2 = where α , β ∈ R Possible approaches to solve parametrised equations 1 use extra parameters as global variables in function m-files 2 define functions to accept extra parameters & use solvers that accept variable length lists of inputs (c.f. bisection.m , newton ) 3 use anonymous functions to encapsulate functions with fixed parameter values We have seen first approach already (c.f. GPS problem)We have seen first approach already (c....
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11-Using-fzero-and-Applications-4UP - fzero Nonlinear...

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