TOMLAB OPTIMIZATION ENVIRONMENT: Tfzero

Tfzero

Purpose

MEX interface for Tfzero, TOMLAB fzero routine

Find a zero for f(x) in an interval

Syntax

  [xLow, xUpp, ExitFlag] = Tfzero(xLow, xUpp, Prob, x_0, RelErr, AbsErr)

Description

Tfzero searches for a zero of a function f(X) between the given values xLow and xUpp until the width of the interval (xLow,xUpp) has collapsed to within a tolerance specified by the stopping criterion,

abs(xLow-xUpp) <= 2.*(RelErr*abs(xLow)+AbsErr).

The method used is an efficient combination of bisection and the secant rule and is due to T. J. Dekker.

Input Parameters

      xLow      A  lower bound on the zero x to f(x)
      xUpp      An upper limit on the zero x to f(x)
      Prob      Structure, sent to matlab routine ZeroFunc
      x0        An initial guess on the zero to f(x).
                If empty, x0 is set as the middle point in [xLow,xUpp]
      RelErr    Relative error tolerance, default 1E-7
      AbsErr    Absolute error tolerance, default 1E-14

Output Parameters

      xLow      A  lower limit on the zero x to f(x)
      xUpp      An upper limit on the zero x to f(x)
      ExitFlag  A status flag 1,2,3,4,5

             1  xLow is within the requested tolerance of a zero.
                The interval (xLow,xUpp) collapsed to the requested
                tolerance, the function changes sign in (xLow,xUpp), and
                F(X) decreased in magnitude as (xLow,xUpp) collapsed.

             2  F(xLow) = 0.  However, the interval (xLow,xUpp) may not have
                collapsed to the requested tolerance.

             3  xLow may be near a singular point of F(X).
                The interval (xLow,xUpp) collapsed to the requested tol-
                erance and the function changes sign in (xLow,xUpp), but
                F(X) increased in magnitude as (xLow,xUpp) collapsed, i.e.
                  abs(F(xLow)) .GT. max(abs(F(xLow-IN)),abs(F(xUpp-IN)))

             4  No change in sign of F(X) was found although the
                interval (xLow,xUpp) collapsed to the requested tolerance.
                The user must examine this case and decide whether
                xLow is near a local minimum of F(X), or xLow is near a
                zero of even multiplicity, or neither of these.

             5  Too many (> 500) function evaluations used.

Tfmin

Tlsqr