C# Assignment Question

Can anyone help me for this question??
This is for my college homework and I am lost in this one.
Thank you

Use all programming techniques that you have learnt so far, approximate the root of f(x) = x³ - 3 with the bisection method starting with the interval [1, 2] and use e_step = 0.1 and e_abs = 0.1. Root is 1.4375
Initial Requirement:

We have an initial bound [a, b] on the root, that is, f(a) and (b) have opposite signs.

Iteration Process:

Given the interval [a, b], define c = (a + b)/2. Then

if f(c) = 0 (unlikely in practice), then halt, as we have found a root,
if f(c) and f(a) have opposite signs, then a root must lie on [a, c], so assign b = c,
else f(c) and f(b) must have opposite signs, and thus a root must lie on [c, b], so assign a = c.

Halting Conditions:

There are three conditions which may cause the iteration process to halt:

As indicated, if f(c) = 0.
We halt if both of the following conditions are met:
- The width of the interval (after the assignment) is sufficiently small, that is b - a < e_step, and
- The function evaluated at one of the end point |f(a)| or |f(b)| < e_abs.

If we halt due to Condition 1, we state that c is our approximation to the root. If we halt according to Condition 2, we choose either a or b, depending on whether |f(a)| < |f(b)| or |f(a)| > |f(b)|, respectively.

Try this:

using System;

class Program

{

static void Main()

{

const double estep = 0.1;

const double eabs = 0.1;

double a = 1;

double b = 2;

double fa, fb;

// check initial requirement

fa = GetValue(a);

fb = GetValue(b);

if (Math.Sign(fa) == Math.Sign(fb) || fa == 0 || fb == 0)

{

Console.WriteLine("Initial requirement not met by [{0}, {1}]", a, b);

}

else

{

// start iteration

double c, fc;

while(true)

{

c = (a + b)/2.0;

if (c == 0)

{

Console.WriteLine("Our approximation to the root is {0}", c);

break;

}

fc = GetValue(c);

if (Math.Sign(fa) == -Math.Sign(fc))

{

b = c;

}

else

{

a = c;

}

if ( (b - a) < estep && (Math.Abs(GetValue(a)) < eabs || Math.Abs(GetValue(b)) < eabs))

{

if (Math.Abs(GetValue(a)) < Math.Abs(GetValue(b)))

{

Console.WriteLine("Our approximation to the root is {0}", a);

}

else

{

Console.WriteLine("Our approximation to the root is {0}", b);

}

break;

}

Console.ReadKey();

}

static double GetValue(double d)

{

return d * d * d - 3;

}

1 Reply

Know the answer? Post it — somebody with the same question will find it here.

Vulpes14y ago
Try this:

using System;

class Program
{
static void Main()
{
const double estep = 0.1;
const double eabs = 0.1;
double a = 1;
double b = 2;
double fa, fb;

// check initial requirement
fa = GetValue(a);
fb = GetValue(b);
if (Math.Sign(fa) == Math.Sign(fb) || fa == 0 || fb == 0)
{
Console.WriteLine("Initial requirement not met by [{0}, {1}]", a, b);
}
else
{
// start iteration
double c, fc;

while(true)
{
c = (a + b)/2.0;
if (c == 0)
{
Console.WriteLine("Our approximation to the root is {0}", c);
break;
}

fc = GetValue(c);
if (Math.Sign(fa) == -Math.Sign(fc))
{
b = c;
}
else
{
a = c;
}

if ( (b - a) < estep && (Math.Abs(GetValue(a)) < eabs || Math.Abs(GetValue(b)) < eabs))
{
if (Math.Abs(GetValue(a)) < Math.Abs(GetValue(b)))
{
Console.WriteLine("Our approximation to the root is {0}", a);
}
else
{
Console.WriteLine("Our approximation to the root is {0}", b);
}
break;
}
}

Console.ReadKey();
}
}

static double GetValue(double d)
{
return d * d * d - 3;
}
}