<![CDATA[The computation of eigenvalues for large-scale matrices is a crucial task in various scientific and engineering domains. This research focuses on the performance of numerical techniques, particularly those utilizing Hessenberg matrices, in solving eigenvalue problems. We investigate the efficacy of these methods and their implementation on modern computational platforms. Our study reveals that increasing the size of the Hessenberg matrix significantly enhances the accuracy of eigenvalue approximations. Through extensive simulations and performance evaluations, we demonstrate that larger Hessenberg matrices provide more precise eigenvalue solutions, underscoring the importance of matrix dimension in the computational process. These findings offer valuable insights for optimizing eigenvalue computations in large-scale applications.]]>
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