Development of Calculator for Finding Complex Roots of n-th Degree Polynomials
Abstract: Software as a
learning medium has become a trend in society. The development of science and
technology encourage modernization in every field of education, including
mathematics. One of the mathematical models often used is polynomial equation.
Many mathematicians have done research on solving polynomials by using
numerical algorithms, but only focus on mathematical analysis. In this
research, design and construction of a calculator as a medium of learning has
been done. The calculator is completed by many algorithm such as the quadratic
formula, Cardano, Viete's, Bairstow, revise Baristow, Muller, and combination
algorithms. The alculator was designed by UML approach and implemented on Java
Swing GUI. The test results using black box method showed that 100% of functional calculator can work well. Based
on the average calculation error, cubic polynomial is solved properly by using
Cardano algorithm which the average error is 1.43568059121049E-13%. Revise
Bairstow algorithm showed good performance to find the complex roots of 4th
degree polynomial with an average error is 1.34421873307271E-09% and average of
iteration is 4. The best combination algorithm on solving nth degree
polynomials is Muller-Cardano which has an average error 4.27781615793958E-13%
and Revise Bairstow-Cardano with average number of iteration is 7 iterations.
Keywords: Finding roots
polynomial, calculator, quadratic formula, Cardano, Viete’s, Bairstow, Revised
Bairstow, Muller
Penulis: Yaniar Rahmah,
Sarngadi Palgunadi, Esti Suryani
Kode Jurnal: jptinformatikadd160513
