{"paper":{"title":"On Approximating Functions of the Singular Values in a Stream","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Yi Li","submitted_at":"2016-04-29T03:35:55Z","abstract_excerpt":"For any real number $p > 0$, we nearly completely characterize the space complexity of estimating $\\|A\\|_p^p = \\sum_{i=1}^n \\sigma_i^p$ for $n \\times n$ matrices $A$ in which each row and each column has $O(1)$ non-zero entries and whose entries are presented one at a time in a data stream model. Here the $\\sigma_i$ are the singular values of $A$, and when $p \\geq 1$, $\\|A\\|_p^p$ is the $p$-th power of the Schatten $p$-norm. We show that when $p$ is not an even integer, to obtain a $(1+\\epsilon)$-approximation to $\\|A\\|_p^p$ with constant probability, any $1$-pass algorithm requires $n^{1-g(\\e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08679","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}