Question

Newton invented the Newton-Raphson method for solving an equation. We are going to ask you to write some code to solve equations. To solve an equation of the form x2-3x + 2-0 we start from an initial guess at the solution: say x,-4.5 Each time we have the i'h guess x, we update it as For our equation,f(x) = x2-3x + 2 andf,(x) = 2x-3. Thus, our update equation is x2 - 3x, 2 2x, - 3 We stop whenever f(x)l 10-8:i.e, we are very close to a root of the function.

Answer 1

A)

object HelloWorld {

    def fx(x: Double) : Double = {
        return x * x - 3*x + 2
    }

    def fxDash(x: Double) : Double = {
        return 2* x - 3
    }

    def calculateRoot(x0: Double) : Double = {
        var x = x0
        while(scala.math.abs(fx(x)) > scala.math.pow(10, -8)) {
            x = x - fx(x)/fxDash(x)
        }
        return x
    }

   def main(args: Array[String]) {
      println(calculateRoot(4.5))
   }
}


B)

object HelloWorld {

    def fx(x: Double) : Double = {
        return x * x - 3*x + 2
    }

    def fxDash(x: Double) : Double = {
        return 2* x - 3
    }

    def calculateRootRec(x0: Double) : Double = {

        if(scala.math.abs(fx(x0)) > scala.math.pow(10, -8)) {
            return calculateRootRec(x0 - fx(x0)/fxDash(x0))
        }

        return x0
    }

   def main(args: Array[String]) {
      println(calculateRootRec(4.5))
   }
}

C)

object HelloWorld {

    def fx(x: Double) : Double = {
        return x * x - 3*x + 2
    }

    def fxDash(x: Double) : Double = {
        return 2* x - 3
    }

    def solveEquationNewtonRaphson(f: Double => Double, fDash: Double => Double, x0: Double) : Double = {

        if(scala.math.abs(f(x0)) > scala.math.pow(10, -8)) {
            return solveEquationNewtonRaphson(f, fDash, x0 - f(x0)/fDash(x0))
        }

        return x0
    }

   def main(args: Array[String]) {
      println(solveEquationNewtonRaphson(fx, fxDash, 4.5))
   }
}

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