ZOOMIN - Scalar Zero Finders

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ZOOMIN is a collection of scalar zero finders, based primarily on a book by Joseph Traub. The wide variety of methods include special rules for polynomials, multiple roots, bisection methods, and methods that use no derivative information.

Reference 1:
Joseph Traub,
Iterative Methods for the Solution of Equations,
Prentice Hall, 1964.

Files you may copy include:

zoomin.f90, the source code;
zoomin_prb.f90, the calling program;
zoomin_prb.out, the sample output.
The list of routines includes:

BISECT carries out the bisection method.
BRENT implements the Brent bisection-based zero finder.
CAP_PHI_03 implements the Traub capital Phi(0,3) method.
CAP_PHI_21 implements the Traub capital PHI(2,1) function.
CHEBYSHEV implements Chebyshev's method.
DAGGER_E12 implements the dagger E 1,2 algorithm.
E3 implements the Traub E3 method.
E4 implements the Traub E4 method.
EULER implements the Euler method.
HALLEY1 implements Halley's method.
HALLEY2 implements Halley's method, with finite differences.
HALLEY_SUPER implements the super Halley method.
HANSON implements the Hanson and Patrick method.
JARRATT implements the Jarratt fourth order method.
JARRATT2 implements the inverse-free Jarratt fourth order method.
KING implements a family of fourth order methods.
LAGUERRE implements the Laguerre rootfinding method for polynomials.
MIDPOINT implements the midpoint method.
MULLER implements Muller's method.
NEWTON implements Newton's method.
NEWTON_MOD implements the modified Newton method.
NEWTON_SEC implements the Newton - secant method.
OSTROWSKI_SQRT implements the Ostrowski square root method.
PERP_E_12 implements the Traub E 1,2 algorithm.
PERP_E_21 implements the Traub perp E 21 method.
PHI_12 implements the Traub capital PHI(1,2) method.
PSI_21 implements the Traub PSI 2,1 method.
PSI_12 implements the Traub PSI 1,2 method.
R_SWAP switches two real values.
RED_CAP_PHI_04 implements the Traub reduced capital PHI(0,4) method.
REGULA implements the Regula Falsi method.
RHEIN1 implements the Rheinboldt bisection - secant method.
RHEIN2 implements the Rheinboldt bisection - secant - inverse quadratic method.
SCRIPT_E2 implements the Traub script E - 2 function.
SCRIPT_E3 implements the Traub script E - 3 function.
SCRIPT_E4 implements the Traub script E - 4 function.
SECANT implements the secant method.
SECANTX carries out the extended secant algorithm.
STAR_E12 implements the Traub *E12 method.
STAR_E21 implements the Traub *E21 method.
STEFFENSON implements Steffenson's method.
STIRLING implements Stirling's method.
T14 implements the Traub fourteenth function.
T15 implements the Traub fifteenth function.
T16 implements the Traub sixteenth function.
T_FAMILY1 implements the Traub first family of iterations.
T_FAMILY2 implements the Traub second family of iterations.
TE11F implements the Traub *E - 1,1(f) function.
TE2U implements the Traub E - 2(u) function.
TIMESTAMP prints the current YMDHMS date as a time stamp.
TPHI1U implements the Traub phi - 1,1(u) function.
TRAUB1 implements the Traub first method.
TRAUB4 implements the Traub fourth method.
TRAUB8 implements the Traub eighth function.
TRAUB9 implements the Traub ninth method.
TRAUB_OSTROWSKI implements the Traub-Ostrowksi method.
TT1F implements the Traub type 1 functions 10 and 11.
TTHIP implements the Traub third function.
VANDEV implements the Van de Vel iteration.
VANDEV2 implements the improved Van de Vel iteration.
WHITTAKER implements the convex acceleeration of Whittaker's method.
WHITTAKER2 implements the double convex acceleeration of Whittaker's method.
ZOOMIN calls all the zero finders for a given problem.

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