How to resolve the algorithm Horner's rule for polynomial evaluation step by step in the Groovy programming language

Published on 12 May 2024 09:40 PM
#Groovy

How to resolve the algorithm Horner's rule for polynomial evaluation step by step in the Groovy programming language

Table of Contents

Problem Statement

A fast scheme for evaluating a polynomial such as: when is to arrange the computation as follows: And compute the result from the innermost brackets outwards as in this pseudocode: Task Description Cf. Formal power series

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Horner's rule for polynomial evaluation step by step in the Groovy programming language

Source code in the groovy programming language

def hornersRule = { coeff, x -> coeff.reverse().inject(0) { accum, c -> (accum * x) + c } }


def coefficients = [-19g, 7g, -4g, 6g]
println (["p coefficients":coefficients])

def testPoly = hornersRule.curry(coefficients)
println (["p(3)":testPoly(3g)])
println (["p(0)":testPoly(0g)])

def derivativeCoefficients = { coeff -> (1..<(coeff.size())).collect { coeff[it] * it } }
println (["p' coefficients":derivativeCoefficients(coefficients)])

def testDeriv = hornersRule.curry(derivativeCoefficients(coefficients))
println (["p'(3)":testDeriv(3g)])
println (["p'(0)":testDeriv(0g)])

def newtonRaphson = { x, f, fPrime ->
    while (f(x).abs() > 0.0001) {
        x -= f(x)/fPrime(x)
    }
    x
}

def root = newtonRaphson(3g, testPoly, testDeriv)
println ([root:root.toString()[0..5], "p(root)":testPoly(root).toString()[0..5], "p'(root)":testDeriv(root).toString()[0..5]])

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