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SOLVING COMPLEX SYSTEMS USING SPREADSHEETS: A

MATRIX DECOMPOSITION APPROACH

Kenneth E. Dudeck, Associate Professor of Electrical Engineering

Pennsylvania State University, Hazleton Campus

Abstract

Many problems in engineering design and analysis, such as sinusoidal driven electrical circuits, produce a set of complex linear simultaneous equations. This set of equations form a complex system. Many algorithms have been developed to solve this system by finding the complex matrix inverse. [1] – [4]

This paper describes an approach using a spreadsheet, such as Excel. By using this approach, students can use the spreadsheet without the additional cost of purchasing additional software. Excel does not have complex math or complex matrix functions operations, but has real matrix functions. The algorithm is implemented by the decomposition of the complex matrix into real matrices and programming the spreadsheet using the built in real matrix functions afforded by the spreadsheet package.

Approach

A system of complex equations can be expressed as:

Zv=k , (1)

where Z is a complex square matrix of size n, v is the complex unknown vector and k is the complex system constant vector. The matrix system has the form below:

 z11 K z1n  v1   k1        M O M  M  =  M   z L z  v   k   n1 nn  n   n

The solution to this system, v, can be found if the inverse of Z, Z-1, is known.

Z-1 Z v = Z-1 k

“Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education”

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Dudeck, K. (2005, June), Solving Complex Systems Using Spreadsheets Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--14679