broyden: Computes root of function via Broyden's Inverse Update Method

In randall-romero/CompEconR: An R version of Miranda & Fackler's CompEcon toolbox for MATLAB

Description

Computes root of function via Broyden's Inverse Update Method

Usage

broyden(f, x, ..., opt = list(tol = sqrt(.Machine$double.eps), maxit = 100,
  maxsteps = 25, initb = NULL, initi = FALSE, showiters = FALSE))

Arguments

f	function, R^d –> R^d
x	d-array, initial guess for root
...	additional arguments to pass to f
opt	list, options to control rootfinding process tol convergence tolerance maxit maximum number of iterations maxsteps maximum number of backsteps initb an initial inverse Jacobian approximation matrix initi if initb is empty, use the identity matrix to initialize ( if FALSE, a numerical Jacobian will be used) showiters display results of each iteration if TRUE

Value

A list with fields

• x d-array, root of f

• fval d-array, value of f at solution

• fjacinv d.d matrix, inverse of Jacobian estimate

Author(s)

Randall Romero-Aguilar, based on Miranda & Fackler's CompEcon toolbox

References

Miranda, Fackler 2002 Applied Computational Economics and Finance

Examples

broyden(function(x) (x-2)^3, 4)
broyden(function(x) (x-2)^3, 3, opt = list(showiters=TRUE))

# Compute fixedpoint of f(x1,x2)= [x1^2 + x2^3;   x1*x2 - 0.5]
# Initial values [x1,x2] = [-1,-1].  True fixedpoint is x1 = -(1/8)^(1/5),  x2 = 1/(2*x1).
broyden(function(x) c(x[1]^2 + x[2]^3, x[1]*x[2] - 0.5), c(-1,-1))

randall-romero/CompEconR documentation built on May 26, 2019, 10:56 p.m.