What Is Optimization Toolbox?

fzeroAlgorithmLimitationsReferencesThe fzero command is an M-file. The algorithm, which was originatedby T. Dekker, uses a combination of bisection, secant, and inversequadratic interpolation methods. An Algol 60 version, with someimprovements, is given in [1]. A Fortran version, upon which the fzeroM-file is based, is in [2].The fzero command finds a point where the function changes sign. Ifthe function is continuous, this is also a point where the function hasa value near zero. If the function is not continuous, fzero may returnvalues that are discontinuous points instead of zeros. For example,fzero(@tan,1) returns 1.5708, a discontinuous point in tan.Furthermore, the fzero command defines a zero as a point where thefunction crosses the x-axis. Points where the function touches, but doesnot cross, the x-axis are not valid zeros. For example, y = x.^2 is aparabola that touches the x-axis at 0. Since the function never crossesthe x-axis, however, no zero is found. For functions with no valid zeros,fzero executes until Inf, NaN, or a complex value is detected.[1] Brent, R., Algorithms for Minimization Without Derivatives,Prentice-Hall, 1973.[2]Forsythe,G.E.,M.A.Malcolm,andC.B.Moler,Computer Methodsfor Mathematical Computations, Prentice-Hall, 1976.See Also@ (function_handle), \ (matrix left division), fminbnd, fsolve,optimset, optimtool, roots, anonymous functions8-128