Selection of Testing Interpolation and Diff. Function

Interpolation Cubic Spline, Akima Spline, Hermit Spline and Function Numerical Differential

This is a collection of functions which are very useful for testing interpolation and differential functions.

Testing function features:

Classical mathematical functions made up of elementary functions, including trigonometric periodic functions

Abnormal functions which generate rapid oscillations in some breaking points. It is usually a composition of trigonometric (periodic functions) and non linear functions for example:- , etc.

The second type of abnormal functions are a composition of rapidly growing functions and periodic functions. The resultant function has a rapid increase in value at specific points or when the value of x is increasing.

These functions can be unpredictable for interpolations in some areas caused by a very rapidly changing function value. This will create a situation in which there is not enough information/points to construct a good interpolation. This can generate situations where the interpolation does not show some of the functions maximum or minimum points.

In these situations the only solution is to increase the number of points.

List of Functions

Function	Comments	Cubic	Hermite	Akima	Diffe.
	Classical combination of trigonometric functions	P	P	P	-
	Combination of trigonometric functions	-	-	-	-
	Function has rapid changes - from down to up at points where the sine function equals one ( ). For these points the first differential is not defined as it is infinite.	P	P	P	-
	Combination of trigonometric functions	-	-	-	P
	Composition of Square Root and Sine. Increasing value of x, distance between adjacent maximum and minimum will be increased.	P	P	P	-
	Composition of Logarithm and Trigonometric functions. When x moving close to zero and then the distances between maximums rapidly decreases.	P	P	P	-
	Increasing the value of x - the distance between maximum and minimum will be decreased.	P	P	P	P
	Combination of trigonometric and quadratic functions with many maximums and minimums.	P	P	P	P
	Combination of Exponential functions	-	-	-	P
	Combination of Exponential and Trigonometric functions.	-	-	-	P
	Function which generates saw tooth shape close to zero. When falling to zero the frequency of function's oscillation will be increased but the amplitude is reduced.	P	P	P	-
	An increasing the value of x will increase the frequency of function oscillation.	P	P	P	P
	The function is not defined when x equals zero	-	-	-	P
	First deferential is symmetrical compared to function	-	-	-	P
	Standard rational function	-	-	-	P
	Power function	-	-	-	-