{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T20:02:43Z","timestamp":1790712163409,"version":"4.1.0"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of Kansa's well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data-dependent meshless selection of test and trial spaces. The new method satisfies the assumptions of the background theory, and numerical experiments demonstrate its stability.<\/jats:p>","DOI":"10.1137\/06067300x","type":"journal-article","created":{"date-parts":[[2008,3,7]],"date-time":"2008-03-07T18:06:03Z","timestamp":1204913163000},"page":"1097-1115","source":"Crossref","is-referenced-by-count":68,"title":["Stable and Convergent Unsymmetric Meshless Collocation Methods"],"prefix":"10.1137","volume":"46","author":[{"given":"Leevan","family":"Ling","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert","family":"Schaback","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,3,7]]},"reference":[{"key":"R1","unstructured":"S. N. Atluri and S. P. Shen,\n                      The Meshless Local Petrov-Galerkin (MLPG) Method\n                      , Tech Science Press, Encino, CA, 2002."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02162565"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1023\/A:1018916902176"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(97)10104-7"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0955-7997(00)00034-5"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(99)00255-6"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(00)00071-7"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(90)90270-T"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(90)90271-K"},{"key":"R10","unstructured":"O. A. Ladyzhenskaya,\n                      The boundary value problems of mathematical physics\n                      , Appl. Math. Sci. 49, Springer-Verlag, New York, 1985 (translated from Russian by Jack Lohwater [Arthur J. Lohwater])."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/j.enganabound.2005.08.008"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(92)90175-H"},{"key":"R13","unstructured":"R. Schaback,\n                      On the versatility of meshless kernel methods\n                      , in Advances in Computational & Experimental Engineering & Sciences 428, S.N. Atluri, D.E. Beskos, and D. Polyzos, eds., Universit\u00e4t G\u00f6ttingen, 2003."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/050633366"},{"key":"R15","unstructured":"R. Schaback,\n                      Unsymmetric Meshless Methods for Operator Equations\n                      , 2006, http:\/\/www.num.math.uni-goettingen.de\/schaback."},{"key":"R16","doi-asserted-by":"crossref","unstructured":"H. Wendland,\n                      Scattered Data Approximation\n                      , Cambridge University Press, London, 2005.","DOI":"10.1017\/CBO9780511617539"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1007\/BF02836101"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/06067300X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:12:59Z","timestamp":1787325179000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/06067300X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/06067300X"],"URL":"https:\/\/doi.org\/10.1137\/06067300x","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}