Site Statistics  |   Contact  |   About Us       Saturday, January 25, 2020

HOME › AREAS OF EXPERTISE › Optimization Algorithms › ~ Bisection Method

 "Optimization Solutions" Optimization Bisection Method
 Minimum = x = 0.273475646972656
 Value = f(x) = -0.289859784079365

 f(x) = 1.6 x3 + 3x2 - 2x [ Interval Low: ] [ Interval High: ] [ Tolerance: 1.0e-5]

IMPLEMENTATION
Bisection Method Optimization

The bisection method for finding the minimum starts with an interval that contains the minimum and then divides that interval into two parts to zoom in on the minimum location.

Algorithm Creation

The steps to apply the bisection method to find the minimum of the function f(x) are listed below,

 Choose xa and xb as two guesses for the minimum such that f'(xa)f'(xb) < 0 Set xm = x(a + xb) / 2 as the mid point between xa and xb. Repeat the above steps until the specified accuracy is reached.

Testing the Bisection Method

We use the bisection method to find the minimum of a nonlinear function. To test it out as defined above, a new TestBisection() static method has been added and executed. Supporting code and methods are not shown.

static void TestBisection();
{
ListBox1.Items.Clear();
ListBox2.Items.Clear();
double result = Optimization.Bisection(f, t1, t2, 1.0e-5);
}

In order to test the bisection method a nonlinear function f(x)=1.6x3+3x2-2x was created. We can now test the minimum and function values based on different intervals. The user can manipulate interval values as desired

 Other Implementations...

 Object-Oriented Implementation Graphics and Animation Sample Applications Ore Extraction Optimization Vectors and Matrices Complex Numbers and Functions Ordinary Differential Equations - Euler Method Ordinary Differential Equations 2nd-Order Runge-Kutta Ordinary Differential Equations 4th-Order Runge-Kutta Higher Order Differential Equations Nonlinear Systems Numerical Integration Numerical Differentiation Function Evaluation

 You are viewing this tab ↓

Math, Analysis & More,
established expertise..."

EIGENVALUE SOLUTIONS...
Eigen Inverse Iteration
Rayleigh-Quotient Method

INTERPOLATION APPLICATIONS...
Cubic Spline Method
Newton Divided Difference

 Applied Mathematical Algorithms
 Complex Functions A complex number z = x + iy, where... Complex Functions Non-Linear Systems Non-linear system methods... Non Linear Systems Differentiation Construction of differentiation... Differentiation Integration Consider the function where... Integration