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Here's a simple Polynomial class which also includes a method to solve it using the Newton-Raphson method:

using System;

using System.Text;

public class Polynomial

{

int degree;

double[] terms;

public Polynomial(double[] terms)

{

this.terms = terms;

this.degree = terms.Length - 1;

}

public Polynomial Differentiate()

{

if (degree == 0) return new Polynomial(new double[] { 0.0 });

double[] deriv = new double[degree];

int deg = degree;

int len = terms.Length;

for (int i = 0; i < len - 1; i++)

{

deriv[i] = (deg--) * terms[i];

}

return new Polynomial(deriv);

}

public double Evaluate(double x)

{

double val = 0;

int len = terms.Length;

double pow = 1;

for (int i = len - 1; i >= 0; i--)

{

if (terms[i] != 0)

{

val += terms[i] * pow;

}

pow *= x;

}

return val;

}

public double Solve (double guess)

{

Polynomial deriv = this.Differentiate();

double x0 = guess;

double x1 = x0;

double diff;

bool convergent = true;

int count = 0;

{

double divisor = deriv.Evaluate(x0);

if (divisor == 0)

{

convergent = false;

break;

}

x1 = x0 - this.Evaluate(x0)/divisor;

diff = Math.Abs(x1 - x0);

x0 = x1;

count++;

}

while (diff > 0.00000001 && count < 100);

if (!convergent || count == 100)

{

Console.WriteLine("May be non-convergent. Stopped after " + count

+ " iterations");

}

return x1;

}

public override string ToString()

{

StringBuilder sb = new StringBuilder();

int deg = degree + 1;

int len = terms.Length;

int first = -1;

for (int i = 0; i < len; i++)

{

deg--;

if (terms[i] == 0 && len != 1) continue;

if (first == -1) first = i;

if (terms[i] >= 0)

{

if (i > first) sb.Append(" + ");

if (terms[i] != 1 || i == len - 1) sb.Append(terms

[i].ToString());

}

else

{

sb.Append(" - ");

if (terms[i] != -1 || i == len - 1) sb.Append((-terms

[i]).ToString());

}

if (i < len - 2)

{

sb.Append("x^" + deg.ToString());

}

else if (i == len - 2)

{

sb.Append("x");

}

return sb.ToString();

}

class Newton

{

static void Main()

{

double[] terms = {1, 0, -1, 1}; // x^3 - x + 1

Polynomial p = new Polynomial(terms);

Console.WriteLine("The polynomial is {0}", p);

double result = p.Solve(1);

Console.WriteLine("The method gives a root of " + result);

Console.WriteLine("The residue for this root is " + p.Evaluate

(result));

Console.ReadKey();

}

The output is:

The polynomial is x^3 - x + 1

The method gives a root of -1.32471795724475

The residue for this root is 0

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Vulpes12y ago
Here's a simple Polynomial class which also includes a method to solve it using the Newton-Raphson method:

using System;
using System.Text;

public class Polynomial
{
int degree;

double[] terms;

public Polynomial(double[] terms)
{
this.terms = terms;
this.degree = terms.Length - 1;
}

public Polynomial Differentiate()
{
if (degree == 0) return new Polynomial(new double[] { 0.0 });
double[] deriv = new double[degree];
int deg = degree;
int len = terms.Length;

for (int i = 0; i < len - 1; i++)
{
deriv[i] = (deg--) * terms[i];
}

return new Polynomial(deriv);
}

public double Evaluate(double x)
{
double val = 0;
int len = terms.Length;
double pow = 1;

for (int i = len - 1; i >= 0; i--)
{
if (terms[i] != 0)
{
val += terms[i] * pow;
}
pow *= x;
}

return val;
}

public double Solve (double guess)
{
Polynomial deriv = this.Differentiate();
double x0 = guess;
double x1 = x0;
double diff;
bool convergent = true;
int count = 0;

do
{
double divisor = deriv.Evaluate(x0);
if (divisor == 0)
{
convergent = false;
break;
}
x1 = x0 - this.Evaluate(x0)/divisor;
diff = Math.Abs(x1 - x0);
x0 = x1;
count++;
}
while (diff > 0.00000001 && count < 100);

if (!convergent || count == 100)
{
Console.WriteLine("May be non-convergent. Stopped after " + count

+ " iterations");
}

return x1;
}

public override string ToString()
{
StringBuilder sb = new StringBuilder();
int deg = degree + 1;
int len = terms.Length;
int first = -1;

for (int i = 0; i < len; i++)
{
deg--;
if (terms[i] == 0 && len != 1) continue;
if (first == -1) first = i;
if (terms[i] >= 0)
{
if (i > first) sb.Append(" + ");
if (terms[i] != 1 || i == len - 1) sb.Append(terms

[i].ToString());
}
else
{
sb.Append(" - ");
if (terms[i] != -1 || i == len - 1) sb.Append((-terms

[i]).ToString());
}
if (i < len - 2)
{
sb.Append("x^" + deg.ToString());
}
else if (i == len - 2)
{
sb.Append("x");
}
}

return sb.ToString();
}

}

class Newton
{
static void Main()
{
double[] terms = {1, 0, -1, 1}; // x^3 - x + 1
Polynomial p = new Polynomial(terms);
Console.WriteLine("The polynomial is {0}", p);
double result = p.Solve(1);
Console.WriteLine("The method gives a root of " + result);
Console.WriteLine("The residue for this root is " + p.Evaluate

(result));
Console.ReadKey();
}
}

The output is:

The polynomial is x^3 - x + 1
The method gives a root of -1.32471795724475
The residue for this root is 0