The content introduces an innovative algorithm for maintaining approximate maximum eigenvectors and eigenvalues of matrices under decreasing updates. It addresses the limitations of existing techniques, providing a breakthrough in dynamic algorithms for spectral information maintenance.
The study spans over five decades, with various techniques developed to compute eigenvalues and eigenvectors. The proposed algorithm leverages an oblivious adversary to achieve polylogarithmic update time per non-zeros. By analyzing the influential power method in a dynamic setting, the authors demonstrate significant advancements in maintaining spectral information efficiently.
Furthermore, the content explores connections to positive semi-definite programs and poses open problems related to dynamic algorithms against oblivious and adaptive adversaries. The research contributes significantly to the field by addressing key challenges in maintaining spectral information dynamically.
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by Deeksha Adil... om arxiv.org 02-29-2024
https://arxiv.org/pdf/2402.17929.pdfDiepere vragen