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pracma (version 1.2.0)

newtonRaphson: Rootfinding through Newton-Raphson or Secant.

Description

Finding roots of univariate functions.

Usage

newtonRaphson(fun, x0, dfun = NULL, ...,
       maxiter = 100, tol = .Machine$double.eps^0.5)

secant(fun, a, b, ..., maxiter = 100, tol = .Machine$double.eps^0.5)

Arguments

fun
Function or its name as a string.
x0
starting value for newtonRaphson().
dfun
A function to compute the derivative of f. If NULL, a numeric derivative will be computed.
a
For secant one of the two starting values.
b
Another starting value.
maxiter
maximum number of iterations; default 100.
tol
absolute tolerance; default eps^(1/2)
...
Additional arguments to be passed to f.

Value

  • Return a list with components root, f.root, the function value at the found root, iter, the number of iterations done, and root, and the estimated precision estim.prec

    For both methods the estimated precision is given as the difference to the last solution before stop; this may be misleading.

Details

Well known root finding algorithms for real, univariate, continuous functions.

References

Quarteroni, A., R. Sacco, and F. Saleri (2007). Numerical Mathematics. Second Edition, Springer-Verlag, Berlin Heidelberg.

See Also

newtonHorner

Examples

Run this code
# Legendre polynomial of degree 5
lp5 <- c(63, 0, -70, 0, 15, 0)/8
f <- function(x) polyval(lp5, x)
newtonRaphson(f, 1.0)  # 0.9061798459 correct to 10 decimals in 5 iterations
secant(f, 0.9, 1)      # 0.9061798459 correct to 10 decimals in 5 iterations

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