zoomin

zoomin, an Octave code which seeks a root of a scalar function.

The code is based primarily on a book by Joseph Traub.

These routines are each intended to find one of more solutions of an equation in one unknown, written as

f(x) = 0
The wide variety of methods include special rules for polynomials, multiple roots, bisection methods, and methods that use no derivative information.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

zoomin is available in a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

zoomin_test

bisection_integer, an Octave code which seeks an integer solution to the equation F(X)=0, using bisection within a user-supplied change of sign interval [A,B].

bisection_rc, an Octave code which seeks a solution to the equation F(X)=0 using bisection within a user-supplied change of sign interval [A,B]. The procedure is written using reverse communication (RC).

test_zero, an Octave code which defines functions which can be used to test zero finders.

zero_brent, an Octave code which seeks a solution of a scalar nonlinear equation f(x) = 0, by Richard Brent.

zero_itp, an Octave code which finds a zero of a scalar function of a scalar variable, starting from a change of sign interval, using the Interpolate/Truncate/Project (ITP) method, which has faster convergence than the bisection method.

zero_laguerre, an Octave code which uses Laguerre's method to find the zero of a function. The method needs first and second derivative information. The method almost always works when the function is a polynomial.

zero_muller, an Octave code which seeks a root of a nonlinear equation using the Muller method, with complex arithmetic.

zero_rc, an Octave code which seeks solutions of a scalar nonlinear equation f(x) = 0, or a system of nonlinear equations, using reverse communication (RC).

Reference:

  1. Richard Brent,
    Algorithms for Minimization without Derivatives,
    Dover, 2002,
    ISBN: 0-486-41998-3,
    LC: QA402.5.B74.
  2. Harold Deiss,
    ZOOMIN technical report,
    zoomin_report.txt.
  3. Eldon Hansen, Merrell Patrick,
    A Family of Root Finding Methods,
    Numerische Mathematik,
    Volume 27, Number 3, September 1977, pages 257-269.
  4. P Jarratt,
    Some fourth-order multipoint iterative methods for solving equations,
    Mathematics of Computation,
    Volume 20, Number 95, July 1966, pages 434-437.
  5. Richard King,
    A family of fourth order methods,
    SIAM Journal on Numerical Analysis,
    Volume 10, 1973, pages 876-879.
  6. Richard King,
    Improving the van de Vel root-finding method,
    Computing,
    Volume 30, 1983, pages 373-378.
  7. Werner Rheinboldt,
    Algorithms for finding zeros of a function,
    UMAP Journal,
    Volume 2, Number 1, 1981, pages 43-72.
  8. Joseph Traub,
    Iterative Methods for the Solution of Equations,
    ISBN: 0828403120,
    LC: QA297.T7,
    Prentice Hall, 1964.
  9. Hugo vandeVel,
    A method for computing a root of a single nonlinear equation, including its multiplicity,
    Computing,
    Volume 14, 1975, pages 167-171.

Source Code:

Last revised on 16 May 2024.