Package webcab.lib.math.interpolation

The Interpolation module contains several methods for Interpolating and Extrapolating functions of 1 or 2 variables.

See:
Description

Class Summary

Interpolation

Offers several procedures for the Interpolating and Extrapolating functions of 1 or 2 variables.

Exception Summary

InterpolationException

This exception will be thrown to indicate errors in input values for any of the implemented methods.

Package webcab.lib.math.interpolation Description

The Interpolation module contains several methods for Interpolating and Extrapolating functions of 1 or 2 variables. We employ a range of approached include cubic splines, polynomial and rational interpolation for functions with 1 variable and bicubic splines for functions of two variables.

Details of the Functionality Offered

The Interpolation module includes the following features:

• Polynomial Interpolation and extrapolation
• Lagrange's formula - for interpolating a function known at N points with a polynomial of degree N-1.
• Burlisch-Stoer algorithm - interpolates functions using rational functions, this method gives error estimates.
• Cubic Splines - we give algorithms for natural and clamped cubic splines.
• Sorting - efficient techniques are used for finding tabulated values.
• Coefficients of an Interpolating Polynomial
• Matrix method - this method relies upon diagonalizing a matrix (or solving a system of equations), and is of the order N squared.
• Zero method - by evaluating the interpolating polynomial at particular values we deduce the coefficients, this method is of the order N cubed.
• Interpolation and extrapolation in two or more dimensions
• Grid - functions can be interpolated on an n-dimensional grid.
• Bilinear interpolation - we consider a multidimensional interpolation by breaking the problem into successive one dimensional interpolations.
• Accuracy - the use of higher order polynomials to obtain increased accuracy.
• Smoothness - the use of higher order polynomials to enforce smoothness on some of the derivatives.
• Bicubic interpolation - finds an interpolating function with a specified derivatives and cross derivatives which vary smoothly at the grid points.
• Bicubic spline - a special case of Bicubic interpolation involving the use of successive one-dimensional splines.

Classes contained within the Interpolatio module

• Interpolation - Offer interpolation and extrapolation on tabulated functions of one or two variables.