# module Newton

newton.rb

Solves the nonlinear algebraic equation system f = 0 by Newton's method. This program is not dependent on BigDecimal.

To call:

```  n = nlsolve(f,x)
where n is the number of iterations required,
x is the initial value vector
f is an Object which is used to compute the values of the equations to be solved.```

It must provide the following methods:

f.values(x)

returns the values of all functions at x

f.zero

returns 0.0

f.one

returns 1.0

f.two

returns 2.0

f.ten

returns 10.0

f.eps

returns the convergence criterion (epsilon value) used to determine whether two values are considered equal. If |a-b| < epsilon, the two values are considered equal.

On exit, x is the solution vector.

### Public Instance Methods

nlsolve(f,x) click to toggle source

See also Newton

```# File ext/bigdecimal/lib/bigdecimal/newton.rb, line 43
def nlsolve(f,x)
nRetry = 0
n = x.size

f0 = f.values(x)
zero = f.zero
one  = f.one
two  = f.two
p5 = one/two
d  = norm(f0,zero)
minfact = f.ten*f.ten*f.ten
minfact = one/minfact
e = f.eps
while d >= e do
nRetry += 1
# Not yet converged. => Compute Jacobian matrix
dfdx = jacobian(f,f0,x)
# Solve dfdx*dx = -f0 to estimate dx
dx = lusolve(dfdx,f0,ludecomp(dfdx,n,zero,one),zero)
fact = two
xs = x.dup
begin
fact *= p5
if fact < minfact then
raise "Failed to reduce function values."
end
for i in 0...n do
x[i] = xs[i] - dx[i]*fact
end
f0 = f.values(x)
dn = norm(f0,zero)
end while(dn>=d)
d = dn
end
nRetry
end```