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.

Prices
WebCab Functions v2.0 J2SE Edition
Single Developer License
 $119
4 Developer Team License
 $203
Site Wide Developer License
 $405
Demo License (limited functionality)
 $0
Prices are expressed in US Dollars.
Product Details
This suite includes the following features:

Interpolation Module

  • 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




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.

Prerequisites

  • An Operating System running JavaTM
  • Pentium III® 500 Mhz
  • 128MB RAM

Software requirements:
  • JDK 1.3 or compatible
Compatibility
Operating System for Deployment:
  • Windows 2003, XP, 2000, NT, 9x
  • Sun Solaris
  • Linux
  • IBM AIX

Built Using:

  • JavaTM 2 SDK Standard Edition 1.3.1/1.4.x
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