This suite includes the following features: Interpolation ModulePolynomial 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 ModuleInterval 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. This is a powerful feature since it allows you to perform calculations in a DBMS manner without having to code the C# to SQL database transaction yourself as it is all done by the ASP within the .NET Framework managed server side environment.
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