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<html>
<head>
<title>
ZOOMIN - Scalar Zero Finders
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ZOOMIN <br> Scalar Zero Finders
</h1>
<hr>
<p>
<b>ZOOMIN</b>
is a FORTRAN90 library which
seeks a root of a scalar function.
</p>
<p>
The library is based primarily on a book by Joseph Traub.
</p>
<p>
These routines are each intended to find one of more solutions
of an equation in one unknown, written as
<blockquote><b>
f(x) = 0
</b></blockquote>
The wide variety of methods include
special rules for polynomials, multiple roots, bisection methods,
and methods that use no derivative information.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/bisection_integer/bisection_integer.html">
BISECTION_INTEGER</a>,
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].
</p>
<p>
<a href = "../../f_src/brent/brent.html">
BRENT</a>,
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.
</p>
<p>
<a href = "../../f_src/test_zero/test_zero.html">
TEST_ZERO</a>,
a FORTRAN90 library which
defines functions which can be used to test zero finders.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Richard Brent,<br>
Algorithms for Minimization without Derivatives,<br>
Dover, 2002,<br>
ISBN: 0-486-41998-3,<br>
LC: QA402.5.B74.
</li>
<li>
Eldon Hansen, Merrell Patrick,<br>
A Family of Root Finding Methods,<br>
Numerische Mathematik,<br>
Volume 27, Number 3, September 1977, pages 257-269.
</li>
<li>
P Jarratt,<br>
Some fourth-order multipoint iterative methods for
solving equations,<br>
Mathematics of Computation,<br>
Volume 20, Number 95, July 1966, pages 434-437.
</li>
<li>
Richard King,<br>
A family of fourth order methods,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 10, 1973, pages 876-879.
</li>
<li>
Richard King,<br>
Improving the van de Vel root-finding method,<br>
Computing,<br>
Volume 30, 1983, pages 373-378.
</li>
<li>
Werner Rheinboldt,<br>
Algorithms for finding zeros of a function,<br>
UMAP Journal,<br>
Volume 2, Number 1, 1981, pages 43-72.
</li>
<li>
Joseph Traub,<br>
Iterative Methods for the Solution of Equations,<br>
Prentice Hall, 1964.
</li>
<li>
Hugo vandeVel,<br>
A method for computing a root of a single nonlinear equation,
including its multiplicity,<br>
Computing,<br>
Volume 14, 1975, pages 167-171.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "zoomin.f90">zoomin.f90</a>, the source code;
</li>
<li>
<a href = "zoomin.sh">zoomin.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "zoomin_prb.f90">zoomin_prb.f90</a>, the calling program;
</li>
<li>
<a href = "zoomin_prb.sh">zoomin_prb.sh</a>,
commands to compile, link and run the calling program;
</li>
<li>
<a href = "zoomin_prb_output.txt">zoomin_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BISECT</b> carries out the bisection method.
</li>
<li>
<b>BRENT</b> implements the Brent bisection-based zero finder.
</li>
<li>
<b>CAP_PHI_03</b> implements the Traub capital Phi(0,3) method.
</li>
<li>
<b>CAP_PHI_21</b> implements the Traub capital PHI(2,1) function.
</li>
<li>
<b>CHEBYSHEV</b> implements Chebyshev's method.
</li>
<li>
<b>DAGGER_E12</b> implements the dagger E 1,2 algorithm.
</li>
<li>
<b>E3</b> implements the Traub E3 method.
</li>
<li>
<b>E4</b> implements the Traub E4 method.
</li>
<li>
<b>EULER</b> implements the Euler method.
</li>
<li>
<b>HALLEY1</b> implements Halley's method.
</li>
<li>
<b>HALLEY2</b> implements Halley's method, with finite differences.
</li>
<li>
<b>HALLEY_SUPER</b> implements the super Halley method.
</li>
<li>
<b>HANSEN</b> implements the Hansen and Patrick method.
</li>
<li>
<b>JARRATT</b> implements the Jarratt fourth order method.
</li>
<li>
<b>JARRATT2</b> implements the inverse-free Jarratt fourth order method.
</li>
<li>
<b>KING</b> implements a family of fourth order methods.
</li>
<li>
<b>LAGUERRE</b> implements the Laguerre rootfinding method for polynomials.
</li>
<li>
<b>MIDPOINT</b> implements the midpoint method.
</li>
<li>
<b>MULLER</b> implements Muller's method.
</li>
<li>
<b>NEWTON</b> implements Newton's method.
</li>
<li>
<b>NEWTON_MOD</b> implements the modified Newton method.
</li>
<li>
<b>NEWTON_SEC</b> implements the Newton - secant method.
</li>
<li>
<b>OSTROWSKI_SQRT</b> implements the Ostrowski square root method.
</li>
<li>
<b>PERP_E_12</b> implements the Traub E 1,2 algorithm.
</li>
<li>
<b>PERP_E_21</b> implements the Traub perp E 21 method.
</li>
<li>
<b>PHI_12</b> implements the Traub capital PHI(1,2) method.
</li>
<li>
<b>PSI_21</b> implements the Traub PSI 2,1 method.
</li>
<li>
<b>PSI_12</b> implements the Traub PSI 1,2 method.
</li>
<li>
<b>R8_SWAP</b> switches two real values.
</li>
<li>
<b>RED_CAP_PHI_04</b> implements the Traub reduced capital PHI(0,4) method.
</li>
<li>
<b>REGULA</b> implements the Regula Falsi method.
</li>
<li>
<b>RHEIN1</b> implements the Rheinboldt bisection - secant method.
</li>
<li>
<b>RHEIN2</b> implements the Rheinboldt bisection - secant - inverse quadratic method.
</li>
<li>
<b>SCRIPT_E2</b> implements the Traub script E - 2 function.
</li>
<li>
<b>SCRIPT_E3</b> implements the Traub script E - 3 function.
</li>
<li>
<b>SCRIPT_E4</b> implements the Traub script E - 4 function.
</li>
<li>
<b>SECANT</b> implements the secant method.
</li>
<li>
<b>SECANTX</b> carries out the extended secant algorithm.
</li>
<li>
<b>STAR_E12</b> implements the Traub *E12 method.
</li>
<li>
<b>STAR_E21</b> implements the Traub *E21 method.
</li>
<li>
<b>STEFFENSON</b> implements Steffenson's method.
</li>
<li>
<b>STIRLING</b> implements Stirling's method.
</li>
<li>
<b>T14</b> implements the Traub fourteenth function.
</li>
<li>
<b>T15</b> implements the Traub fifteenth function.
</li>
<li>
<b>T16</b> implements the Traub sixteenth function.
</li>
<li>
<b>T_FAMILY1</b> implements the Traub first family of iterations.
</li>
<li>
<b>T_FAMILY2</b> implements the Traub second family of iterations.
</li>
<li>
<b>TE11F</b> implements the Traub *E - 1,1(f) function.
</li>
<li>
<b>TE2U</b> implements the Traub E - 2(u) function.
</li>
<li>
<b>TPHI1U</b> implements the Traub phi - 1,1(u) function.
</li>
<li>
<b>TRAUB1</b> implements the Traub first method.
</li>
<li>
<b>TRAUB4</b> implements the Traub fourth method.
</li>
<li>
<b>TRAUB8</b> implements the Traub eighth function.
</li>
<li>
<b>TRAUB9</b> implements the Traub ninth method.
</li>
<li>
<b>TRAUB_OSTROWSKI</b> implements the Traub-Ostrowksi method.
</li>
<li>
<b>TT1F</b> implements the Traub type 1 functions 10 and 11.
</li>
<li>
<b>TTHIP</b> implements the Traub third function.
</li>
<li>
<b>VANDEV</b> implements the Van de Vel iteration.
</li>
<li>
<b>VANDEV2</b> implements the improved Van de Vel iteration.
</li>
<li>
<b>WHITTAKER</b> implements the convex acceleeration of Whittaker's method.
</li>
<li>
<b>WHITTAKER2</b> implements the double convex acceleeration of Whittaker's method.
</li>
<li>
<b>ZOOMIN</b> calls all the zero finders for a given problem.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 13 November 2005.
</i>
<!-- John Burkardt -->
</body>
</html>