Volume 20 No 12 (2022)
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A Critical Analyzation of the Comparison of Solutions of Matrix Eigenvalue Problems
Shalu Panwar, Jatinder Saini
Abstract
Eigenvalues play quite an important role in differential equations and the real life. Several phenomena depend upon the eigenvalues (frequency) such as wobbling and collapsing of the bridges, analyzation of the stable and unstable, study of rotatory bodies, vibrating bodies, and their small oscillations, and many more. In this paper we will be observing different methods and their rate of convergence, algorithms, and efficiency. The focus will be on the QR method being the most efficient method in its converging power, efficiency, computational cost, and algorithms. For this we will be looking at some of the basics of the eigenvalues and the matrices as well.
Keywords
QR algorithm; Power method; Rayleigh quotient; Jacobi method; Eigenvalues; Convergence; Algorithm
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