WebCab Functions for Delphi - add 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; to your .NET, COM, and XML Web service Applications.

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.

Here are some key features of "Functions NET":

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 has the following technology aspects:
· 3-in-1: .NET, COM, and XML Web services - Three DLLs, Three API Docs, Three Sets of Client Examples all in 1 product. Offering a 1st class .NET, COM, and XML Web service product implementation.
· Extensive Client Examples - Multiple client examples including .NET (C#, VB.NET, C++.NET), COM and XML Web services (C#, VB.NET)
· ADO Mediator - The ADO Mediator assists the .NET developer in writing DBMS enabled applications by transparently combining the financial and mathematical functionality of our .NET components with the ADO.NET Database Connectivity model.
· Compatible Containers - Visual Studio 6 (incl. Visual Basic 6, Visual C++ 6), Visual Studio .NET (incl. Visual Basic .NET, Visual C#.NET, and Visual C++.NET), Borland's C++ Builder (incl. C++Builder, C++BuilderX, C++ 2005), Borland Delphi 3 - 2005, Office 97/2000/XP/2003.
· ASP.NET Web Application Examples - We provide an ASP.NET Web Application example which enables you to quickly test the functionality within this .NET Service.
· ASP.NET Examples with Synthetic ADO.NET - we use a ASP.NET service to perform component calculations on SQL database columns from a remote DBMS. We apply a component's function to certain rows from the database and list the output in HTML format.


Requirements:

· .NET Framework v1.x