Wilkinson-Like Generalized Multishift QR Algorithm for Large and Dense Matrices

By : Fauzia Shaheen , Najmuddin Ahmad , Farah Deeba

Page No: 213-230

Abstract:
This study investigates advanced 𝑄𝑅 algorithmic strategies for the efficient computation of eigenvalues in large and dense matrices. Emphasis is placed on gen eralised shift techniques and convergence criteria to enhance numerical stability and performance. A novel generalisation of the modified Wilkinson-like multi-shift method is proposed for real Hessenberg matrices, incorporating a structured sequence of House holder transformations. The proposed methodology is evaluated through numerical experiments designed to assess its accuracy and efficiency. All computational results are obtained using MATLAB R2020a.

Authors
Fauzia Shaheen: Integral University, Lucknow, 
Najmuddin Ahmad: Integral University, Lucknow, 
Farah Deeba:  Integral University, Lucknow, 
 

DOI: https://doi.org/10.32381/IAPQRT.2026.50.02.5