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# WebCab Functions (J2EE Edition)

EJB Suite offering refined numerical procedures to either construct a function of one or two variables from a set of points (i.e.

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# Features of WebCab Functions (J2EE Edition)

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 (with 1, 2, 4 or site-wide license) allowing the developer to plug-in a wide range of GUI functionality (including charts/graphs) into their client applications
• EAR Files - we provide individual customized EAR files for the most widely used application servers including IBM WebSphere 4.0/5.0, BEA WebLogic 6.1/7.0, Oracle 9iAS, Sun ONE AppServer 7, Ironflare Orion 1.5.2/1.6.0, Borland AppServer 5.0, Sybase EAServer 3.6 and JBoss 2.4.4/3.0.0
• Self-Deploy - the relevant servers EAR file will be self-deployed onto supported local application servers during the installation of the self-install package. The supported application servers include IBM WebSphere 4.0/5.0, BEA WebLogic 6.1/7.0, Oracle 9iAS, Borland AppServer 5.0, Ironflare Orion 1.5.2/1.6.0 and JBoss 2.4.4/3.0.0
• JDBC Mediator - A server side EJB component which mediates between an EJB component, clients and DBMS. The mediator moves most of a clients JDBC calls to the server and hence greatly increases the speed of JDBC client applications.
• Web Application Example - A JSP interactive HTML interface which enables you to test every component method directly from your browser.
• Synthetic JDBC - we use a JSP component to perform EJB calculations on SQL database columns from a remote DBMS. We apply an EJB function to certain rows from the database and list the output in HTML format. This is a powerful feature since it allows you to perform calculations in a JDBC manner without having to code the EJB-to-JDBC transaction yourself as it is all done by the JSP within the Application Server.
• UML Models - to assist system architects we provide UML diagrams of this component