Description
Offers computationally convenient and effective schemes of
interpolation and extrapolation. These methods are ideal for any
system that needs to work with functions which are stored in tabular form.
We include the methods of Newton polynomials, Lagrange's formula,
Burlisch-Stoer algorithm, Cubic splines (natural and free) and Bicubic
interpolation. We also consider algorithms for finding the coefficients of an
interpolation function and interpolation in higher dimensions.
Product Details
This suite 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
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