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METHODS
Newton-Raphson Method

The Newton-Raphson method is the most popular method for solving nonlinear equations. This method is, in general, very suitable for its convenience and computation efficiency.

The Newton-Raphson method uses the following iteration relation:

 xn + 1 = xn - f (xn) / f '(xn)

Where f '(xn) is the first derivative of function f(x).

Starting with the initial value, xn, it is possible to find the next guess, xn + 1, by using the above iteration relation. This process can be repeated until the solution within a given tolerance is found.

 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

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EIGENVALUE
SOLUTIONS...

> Rayleigh-Quotient Method

> Cubic Spline Method

 Applied Mathematical Algorithms ComplexFunctions NonLinear Differentiation Integration
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