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OVERVIEW
Integration of Functions

FUNCTION EVALUATION...

Many mathematical functions used in numerical computation are defined by an integral, a recurrence formula, or a series expansion. FUNCTION CONCEPT...

A function in Smalltalk (the language we used for implementation) can be readily implemented with a block closure. Block closures in Smalltalk are treated like objects; thus, they can be manipulated as any other objects. For example, the one-variable function defines as

 f(x) = 1 / x,

can be implemented as

 f := [:x | 1 / x]

Funtion evaluation is heavily used in the area of statistics. While we did not get a chance to get involved in a mineral application applying these techniques, we believe is worth sharing with our readers the importance of its use. We do show our test implementations using Smalltalk as the language of choice.

We chose four function concepts to illustrate our handling of function evaluation: Polynomials, Error Function, Gamma Function and Beta Function.

Please select from the menu  →         FUNCTION EVALUATION IN SMALLTALK  (press to select)

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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