Developing a hybrid root-finding algorithm

Melisa Hendrata
California State University-Los Angeles, Mathematics

This activity is part of the Teaching Computation in the Sciences Using MATLAB Peer Reviewed Teaching Activities collection. (view details)

This activity was selected for the Teaching Computation in the Sciences Using MATLAB Peer Reviewed Teaching Collection

This activity has received positive reviews in a peer review process involving five review categories. The five categories included in the process are

Computational, Quantitative, and Scientific Accuracy
Alignment of Learning Goals, Activities, and Assessments
Pedagogic Effectiveness
Robustness (usability and dependability of all components)
Completeness of the ActivitySheet web page

For more information about the peer review process itself, please see https://serc.carleton.edu/teaching_computation/materials/activity_review.html.

Initial Publication Date: August 16, 2018 | Reviewed: November 19, 2018 (see revision history: 2 events)

Summary

In this project, students will write a code implementing the Bisection and Secant algorithms for approximating a zero of a given function within a certain error tolerance. They will then write a hybrid algorithm combining the strengths of Bisection and Secant methods, and analyze its performance in terms of the convergence and the number of iterations needed to achieve the same degree of accuracy.

Mathematics | College Upper (15-16)

Expand for more detail

Share your modifications and improvements to this activity through the Community Contribution Tool »

Learning Goals

Through this project, students will learn the strengths and weaknesses of different root-finding algorithms, and they will learn how to develop a simple hybrid algorithm that combine the strengths of well-known algorithms. They will also learn to identify linear/superlinear/quadratic convergence of these algorithms through the iterates produced by Matlab.

Context for Use

This project is given in the undergraduate upper division Numerical Analysis course. The course will have to cover the topic of root-finding techniques before this project can be assigned. The technique they learned in this project can be applied or extended to create other hybrid algorithms, e.g. combining Bisection and Newton's algorithms.

Students need to know how to translate the pseudo-code of an algorithm into a working code and be able to write a code with control flow (loops, if-else statement, etc). Students are given two weeks to complete the project.