{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:29:10Z","timestamp":1787336950700,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>When the isotypic subspaces of a representation are viewed as the eigenspaces of a symmetric linear transformation, isotypic projections may be achieved as eigenspace projections and computed using the Lanczos iteration. In this paper, we show how this approach gives rise to an efficient isotypic projection method for permutation representations of distance transitive graphs and the symmetric group.<\/jats:p>","DOI":"10.1137\/s0895479801399778","type":"journal-article","created":{"date-parts":[[2004,3,5]],"date-time":"2004-03-05T21:00:50Z","timestamp":1078520450000},"page":"784-803","source":"Crossref","is-referenced-by-count":13,"title":["Computing Isotypic Projections with the Lanczos Iteration"],"prefix":"10.1137","volume":"25","author":[{"given":"David K.","family":"Maslen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael E.","family":"Orrison","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel N.","family":"Rockmore","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Ethan Bolker, The finite Radon transform, Contemp. Math., Vol. 63, Amer. Math. Soc., Providence, RI, 1987, 27\u20135088b:51009","DOI":"10.1090\/conm\/063\/876312"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-74341-2"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1142\/5019"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"J. Cullum and R. Willoughby,\n                      L\u00e1nczos Algorithms for Large Symmetric Eigenvalue Computations, Vol\n                      . I,\n                      Theory\n                      , Birkh\u00e4user Boston, Boston, MA, 1985.","DOI":"10.1007\/978-1-4684-9190-6"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"P. Diaconis,\n                      Group Representations in Probability and Statistics\n                      , Institute of Mathematical Statistics, Hayward, CA, 1988.","DOI":"10.1214\/lnms\/1215467407"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347251"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"Persi Diaconis, Daniel Rockmore, Efficient computation of isotypic projections for the symmetric group, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Vol. 11, Amer. Math. Soc., Providence, RI, 1993, 87\u201310494g:20022","DOI":"10.1090\/dimacs\/011\/06"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539792240121"},{"key":"R9","volume-title":"Abstract algebra","author":"Dummit David","year":"1991"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"W. Gentleman and G. Sande,\n                      Fast Fourier transforms for fun and profit\n                      , in Proc. AFIPS, Fall Joint Computer Conference, Vol. 29, Spartan Books, NY, 1966, pp. 563\u2013578.","DOI":"10.1145\/1464291.1464352"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/24\/22\/006"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-98-00964-8"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"David Maslen, Daniel Rockmore, Generalized FFTs\u2014a survey of some recent results, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Vol. 28, Amer. Math. Soc., Providence, RI, 1997, 183\u201323798k:20020","DOI":"10.1090\/dimacs\/028\/13"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-97-00219-1"},{"key":"R15","unstructured":"M. Orrison,\n                      An Eigenspace Approach to Decomposing Representations of Finite Groups\n                      , Ph.D. thesis, Dartmouth College, Hanover, NH, 2001."},{"key":"R16","volume-title":"The symmetric eigenvalue problem","author":"Parlett Beresford","year":"1980"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"Daniel Rockmore, Some applications of generalized FFTs, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Vol. 28, Amer. Math. Soc., Providence, RI, 1997, 329\u201336998e:65116","DOI":"10.1090\/dimacs\/028\/19"},{"key":"R18","unstructured":"B. Sagan,\n                      The Symmetric Group. Representations, Combinatorial Algorithms, and Symmetric Functions\n                      , The Wadsworth & Brooks\/Cole Mathematics Series, Wadsworth & Brooks\/Cole Advanced Books & Software, Pacific Grove, CA, 1991."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9458-7"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511805967"},{"key":"R21","doi-asserted-by":"crossref","unstructured":"Dennis Stanton, Orthogonal polynomials and Chevalley groups, Math. Appl., Reidel, Dordrecht, 1984, 87\u201312886d:22008","DOI":"10.1007\/978-94-010-9787-1_2"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719574"},{"key":"R23","volume-title":"The algebraic eigenvalue problem","author":"Wilkinson J.","year":"1965"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479801399778","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:38:02Z","timestamp":1787333882000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479801399778"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0895479801399778"],"URL":"https:\/\/doi.org\/10.1137\/s0895479801399778","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}