Java Computer Animation for Effective Learning of the Cholesky Algorithm with Transportation Engineering Applications

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, userfriendly, attractive, and useful Java Visualization and Animation Graphical User Interface (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 class-room 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.