|
Numerical Analysis in Excel and VBA
XLNumerical Methods is a library of commonly used numerical methods functions. The functions available in this toolbox are those which are commonly introduced during the junior year of most engineering programs. These functions provide the ability to model and solve systems of equations which are basis of the "rules" that govern the behavior of engineering systems. These rules include systems of algebraic, integral and differential equations. These functions provide the ability to work with either mathematical functions or sets of data. |
 |
|
These functions are typically classified into the following categories:
| Features: |
|
XLNumerical Methods is: |
- Root Finding
- Interpolation
- Curve Fitting
- Linear Algebra
- Non-Linear Algebra
- Integration
- Difference
- Sensitivity
|
|
- Affordable
- Scalable
- Effective
- Innovative
- User Friendly
- Fast
|
Root Finding
Functions for finding a goal for an arbitrary function using forward marching bracketing, and Newton-Raphson convergence to a solution. This function is designed to jump over poles. Also includes a function to find n-roots of an arbitrary function such as an eigenfunction. Another function calculates the n-complex roots of an nth order polynomial.
Interpolation
Functions include nth order polynomial interpolation of data with equally spaced intervals on the independent variable.
Curve Fitting
Functions include an nth order least square polynomial and a 2d 2nd order polynomial for surface regression.
Linear Algebra
Functions include Gauss Elimination and Jacobi methods. This function is especially useful when large number of systems of equations need to be solved in VBA using iterative methods.
Non-linear algebra
Functions include solving a system of nonlinear functions for a solution based on the assumed initial guess. The function uses an nth order Newton Iteration Method. This function is especially useful when systems of equations need to be solved in VBA.
Integration
Functions include 1, 2 and 3 dimensional numerical integration using equally spaced 1st , 2nd, 3rd and 4th order Newton Methods.
Difference
Functions include 1st, 2nd, 3rd, and 4th derivatives for forward, central and backward difference methods assuming equally spaced data points. Both low order and high order difference methods are available. These 24 equations are neatly packaged into 2 low and high order functions.
Sensitivity
Functions calculate the Jacobian matrix of 1st derivatives for m functions of n variables. Also includes a function to determine the system sensitivity map for doing sensitivity analysis about a design point.
Black Box Capability
One feature which is common to many of the functions is the "black box" design. Since many routines require a function evaluation during each pass through the main procedure loop, model equations need to be coded inside the numerical routines. SpreadsheetWorld created an method which allows the user to pass a string representing the mathematical through the argument list. This allows the routines to achieve a total "black box" design, and therefore be compiled as a convenient and secure add-in. Although the black box paradigm presents a slight compromise in speed versus hard-coded functions, it is believed the benefits far outweigh the consequences. To use this feature, the user must learn a very simple syntax in which the string functions must be passed. XLManager provides a utility to help the user in preparing the input string.
Function Verification
An Example Workbook with example templates for using each function on a sample problem is included in the toolbox, as well as on-line help. Functions are designed to work either from Excel or from VBA and can be called inside an iterative loop such as goal seeking, optimization.
 (149KB)
Buy Now at SpreadsheetWorld.com
|
|
XLNumerical Methods 
