{"paper":{"title":"Better bases for kernel spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NA","authors_text":"E. J. Fuselier, F. J. Narcowich, G. B. Wright, J. D. Ward, T. C. Hangelbroek","submitted_at":"2011-11-03T23:42:55Z","abstract_excerpt":"In this article we investigate the feasibility of constructing stable, local bases for computing with kernels. In particular, we are interested in constructing families $(b_{\\xi})_{\\xi\\in\\Xi}$ that function as bases for kernel spaces $S(k,\\Xi)$ so that each basis function is constructed using very few kernels. In other words, each function $b_{\\zeta}(x) = \\sum_{\\xi\\in\\Xi} A_{\\zeta,\\xi} k(x,\\xi)$ is a linear combination of samples of the kernel with few nonzero coefficients $A_{\\zeta,\\xi}$. This is reminiscent of the construction of the B-spline basis from the family of truncated power function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1013","kind":"arxiv","version":1},"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"}