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Broyden secant method
  Applies a Broyden (multidimensional) secant method to find a solution of a system of nonlinear equations.
2025.Feb.16 16:50:43
n, npar No. of variables (equations) and parameters (here, npar = 2n). •
c Coefficients in paraboloid (see below). •
a Constants in paraboloid. •
Initial
values		 Initial values (guesses) for the roots •
itmax, tol, monit Iterations (max.), tolerance (≥ √εmach.), monitoring. •
Test Shows iterations details.

Applies a Broyden technique to a multidimensional secant method to find a solution of a system of n nonlinear equations in n variables. The base problem system is the gradient of a general paraboloid, z = ∑i=1..n ci (x − ai)2, with obvious solution, x = a, a minimum (maximum) if the coefficients, c, are all strictly positive (negative).

References: Plate: Broyden090103

• Dennis, Jr., J. E., and Robert B. Schnabel, 1996, "Numerical methods for unconstrained optimization and nonlinear equations", SIAM, Philadelphia, PA (USA). Google browse. ISBN 0-89871-364-1 (pp 168–174.pdf).

• Heath, Michael T.: one or several nonlinear equations.pdf (=), Lecture Notes (CSciEng, UIUC).

• NAG C05NBF.pdf subroutine (NAG).

• OTC (Optimization Technology Center): Systems of nonlinear equations (ANL & NW Univ.).

• Chemistry Dept.: CH 490/590, Computer Programming for Scientists (Oregon State Univ.).

• Conrad, Eric van Fossen: Latin phrases (Ohio State Univ.).

• Walton, Andrew G.: Solution of nonlinear algebraic equations.pdf (=), Imperial College London.

• 1777-01-03: Poinsot, Louis, birthday.

 
 
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Created: 2009-01-03 — Last modified: 2009-01-04