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Name : Pritam chandra shil
ID: 162-15-7882
Welcome To My
Presentation
Topic : Bisection
Method
Bisection Method
 The Bisection Method slightly modifies
“educated guess” approach of hand
calculation method.
• Suppose we know a function has a root
between a and b. (…and the function is
continuous, … and there is only one root)
Bisection Method
 Keep in mind general approach in
Computer Science: for complex
problems we try to find a uniform simple
systematic calculation
• How can we express the hand
calculation of the preceding in this way?
Bisection method…
 Check if solution lies between a and b…
F(a)*F(b) < 0 ?
• Try the midpoint m: compute F(m)
• If |F(m)| < tol select m as your
approximate solution
• Otherwise, if F(m) is of opposite sign to
F(a) that is if F(a)*F(m) < 0, then b = m.
• Else a = m.
double Sqrt(double c, double tol)
{ double a,b, mid, f;
// set initial boundaries of interval if (c < 1) { a = c;
b = 1}
else { a = 1; b = c}
do {
mid = ( a + b ) / 2.0;
f = mid * mid - c;
if ( f < 0 ) a = mid;
else b = mid;
}
while( fabs( f ) > tol );
return mid;
}
Thank You !!

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Bisection Method

  • 1. Name : Pritam chandra shil ID: 162-15-7882 Welcome To My Presentation
  • 3. Bisection Method  The Bisection Method slightly modifies “educated guess” approach of hand calculation method. • Suppose we know a function has a root between a and b. (…and the function is continuous, … and there is only one root)
  • 4. Bisection Method  Keep in mind general approach in Computer Science: for complex problems we try to find a uniform simple systematic calculation • How can we express the hand calculation of the preceding in this way?
  • 5. Bisection method…  Check if solution lies between a and b… F(a)*F(b) < 0 ? • Try the midpoint m: compute F(m) • If |F(m)| < tol select m as your approximate solution • Otherwise, if F(m) is of opposite sign to F(a) that is if F(a)*F(m) < 0, then b = m. • Else a = m.
  • 6. double Sqrt(double c, double tol) { double a,b, mid, f; // set initial boundaries of interval if (c < 1) { a = c; b = 1} else { a = 1; b = c} do { mid = ( a + b ) / 2.0; f = mid * mid - c; if ( f < 0 ) a = mid; else b = mid; } while( fabs( f ) > tol ); return mid; }