Scalar Zero Finders

ZOOMIN is a FORTRAN90 library which seeks a root of a scalar function.

The library 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.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


ZOOMIN is available in a FORTRAN90 version.

Related Data and Programs:

BISECTION_INTEGER, a FORTRAN90 library 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, a FORTRAN90 library 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.

BRENT, a FORTRAN90 library which contains Richard Brent's routines for finding the zero, local minimizer, or global minimizer of a scalar function of a scalar argument, without the use of derivative information.

TEST_ZERO, a FORTRAN90 library which defines functions which can be used to test zero finders.

ZERO_RC, a FORTRAN90 library which seeks solutions of a scalar nonlinear equation f(x) = 0, or a system of nonlinear equations, using reverse communication.


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

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.

Last revised on 13 November 2005.