Abstract
In this paper, the well-known Cholesky Algorithm (for solving simultaneous linear equations, or SLE) is re-visited, with the ultimate goal of developing a simple, user-friendly, attractive, and useful Java Visualization and Animation Graphical User Inter-face (GUI) software as an additional teaching tool for students to learn the Cholesky factorization in a step-by-step fashion with computer voice and animation. A demo video of the Cholesky Decomposition (or factorization) animation and result can be viewed online from the website: http://www.lions.odu.edu/~imako001/cholesky/demo/index.html. The software tool developed from this work can be used for both students and their instructors not only to master this technical subject, but also to provide a dynamic/valuable tool for obtaining the solutions for homework assignments, class examinations, self-assessment studies, and other coursework related activities. Various transportation engineering applications of SLE are cited. Engineering educators who have adopted “flipped classroom instruction” can also utilize this Java Visualization and Animation software for students to “self-learning” these algorithms at their own time (and at their preferable locations), and use valuable class-meeting time for more challenging (real-life) problems’ discussions. Statistical data for comparisons of students’ performance with and without using the developed Java computer animation are also included.
Highlights
The Cholesky Decomposition (Factorization) Algorithm was presented by Andre Louis Cholesky in an unknown and unpublished 8-page manuscript on December 2, 1910 entitled: On the numerical solutions of systems of linear equations
Cholesky algorithm has been considered as a major building block in the revised SIMPLEX algorithm for solving Linear Programming (LP) problems [3]
In the Fall-2013 semester, the Cholesky method was explained in the traditional class-room instruction format
Summary
The Cholesky Decomposition (Factorization) Algorithm was presented by Andre Louis Cholesky in an unknown and unpublished 8-page manuscript on December 2, 1910 entitled: On the numerical solutions of systems of linear equations. The Cholesky Decomposition Method is widely known [1] [2] and is used to solve systems of Symmetric Positive Definite (SPD) simultaneous linear equations (SLE). SLE has been discussed in Himes-Donnell’s published work in “Speed Prediction Models for Multilane Highways: Simultaneous Equations Approach” [9]. Adu and his colleagues have considered “Applications of SLE to Traffic Flow for a Network of Four One-Way Streets in Kumasi, Ghana” [10]. With the explosions of internet’s capability and availability, it is even more critical to effectively train this future USA-STEM work-force and/or to develop effective STEM related teaching tools to reach a maximum possible number of “distance learners/audiences”
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