We offer refined numerical procedures to either construct a function of one or
two variables from a set of points (i.e. interpolate), or solve an equation of
one variable. The interpolation procedures provided include Newton polynomials,
Lagrange's formula, Burlisch-Stoer algorithm, Cubic splines (natural and free),
Bicubic interpolation and procedures for find the interpolation functions
coefficients. In order to solve an equation we provide the Van Wijngaarden-Dekker-Brent
algorithm, interval bisection method, secant and false position, Newton-Raphson
method and Ridders' method.
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
- 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
- Zero method - by evaluating the interpolating polynomial at particular
values we deduce the coefficients, this method is of the order
- 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
- 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
Equation Solver Module
- Interval Bisection Method - A robust method that always finds a solution
or a singularity inside a bracketed interval.
- Secant Method - Generally this procedure converges and is much faster than the
interval bisection method.
- Brent's Algorithm - The method of choice to find a bracketed root
of a one dimensional equation when you cannot easily compute the function's derivative.
- Ridders' Method - Concise and almost as reliable as Brent's
Algorithm for finding a bracketed root of an equation.
- Method of Regula Falsi - This procedure uses a slight alteration on
the secant method to ensure convergence. The procedure is generally faster than the interval
bisection method and slightly slower than the secant method.
- Newton-Raphson Method - Given a first approximation to a root and the
differential of the function this procedure will always produce a solution. We implement this procedure
for polynomial functions of one variable.
- Fail-Safe Newton-Raphson Method - This method combines the Newton-Raphson method
and the Interval Bisection Method in order to produce very stable and fast convergence. Given a first
approximation to a root and the differential of the function this procedure will always produce a solution.
This product also contains the following features:
- GUI Bundle - we bundle a suite of graphical user interface JavaBean
components allowing the developer to plug-in a wide range of GUI functionality
(including charts/graphs) into their client applications.
- JDBC Mediator - A J2SE Component which mediates between a J2SE component,
its J2SE Clients and the Database server. The JDBC Mediator J2SE classes are
a convenient way of enhancing all financial and mathematical specific
methods with JDBC-based functionality. Check the jdbc subpackage of
every J2SE class for JavaDocs documentation.
- Web Application Example - A Java WAR file which contains a JSP example that
makes use of the functionality provided by our J2SE Component.
- Synthetic JDBC - The JDBC functionality provided by the Web Application
example included within this package. This Web Application is an example of
how to make a JSP client using our J2SE Component while manually
implementing the JDBC code. The JSP Application applies J2SE methods to
certain rows from the database and lists the output in HTML format.