{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T10:25:19Z","timestamp":1776767119607,"version":"3.51.2"},"reference-count":14,"publisher":"American Mathematical Society (AMS)","issue":"214","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n Pseudorandom vectors are of importance for parallelized simulation methods. In this paper a detailed analysis of the compound inversive method for the generation of\n \n \n \n k<\/mml:mi>\n k<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -dimensional uniform pseudorandom vectors, a vector analog of the compound inversive method for pseudorandom number generation, is carried out. In particular, periodicity properties and statistical independence properties of the generated sequences are studied based on the discrete discrepancy of\n \n \n \n s<\/mml:mi>\n s<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -tuples of successive terms in the sequence. The results show that the generated sequences have attractive statistical independence properties for pseudorandom vectors of dimensions\n \n \n \n \n k<\/mml:mi>\n \n \u2264\n \n <\/mml:mo>\n 4<\/mml:mn>\n <\/mml:mrow>\n k\\leq 4<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n .\n <\/p>","DOI":"10.1090\/s0025-5718-96-00706-5","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"749-760","source":"Crossref","is-referenced-by-count":8,"title":["Pseudorandom vector generation by the compound inversive method"],"prefix":"10.1090","volume":"65","author":[{"given":"Frank","family":"Emmerich","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/BF02932576","article-title":"A nonlinear congruential pseudorandom number generator","volume":"27","author":"Eichenauer, J\u00fcrgen","year":"1986","journal-title":"Statist. Hefte","ISSN":"https:\/\/id.crossref.org\/issn\/0932-5026","issn-type":"print"},{"key":"2","doi-asserted-by":"crossref","unstructured":"J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167\u2013176.","DOI":"10.2307\/1403647"},{"issue":"207","key":"3","doi-asserted-by":"publisher","first-page":"293","DOI":"10.2307\/2153575","article-title":"On generalized inversive congruential pseudorandom numbers","volume":"63","author":"Eichenauer-Herrmann, J\u00fcrgen","year":"1994","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"4","doi-asserted-by":"crossref","unstructured":"\\bysame, Pseudorandom number generation by nonlinear methods, Internat. Statist. Rev. 63 (1995), 247\u2013255.","DOI":"10.2307\/1403620"},{"key":"5","isbn-type":"print","first-page":"75","article-title":"On inversive congruential generators for pseudorandom numbers","author":"Flahive, Mary","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/0824788052"},{"key":"6","doi-asserted-by":"crossref","first-page":"649","DOI":"10.2140\/pjm.1961.11.649","article-title":"On large deviations of the empiric D. F. of vector chance variables and a law of the iterated logarithm","volume":"11","author":"Kiefer, J.","year":"1961","journal-title":"Pacific J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0030-8730","issn-type":"print"},{"key":"7","series-title":"Encyclopedia of Mathematics and its Applications","isbn-type":"print","volume-title":"Finite fields","volume":"20","author":"Lidl, Rudolf","year":"1983","ISBN":"https:\/\/id.crossref.org\/isbn\/0201135191"},{"issue":"2","key":"8","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/0001-8708(77)90028-7","article-title":"Pseudo-random numbers and optimal coefficients","volume":"26","author":"Niederreiter, Harald","year":"1977","journal-title":"Advances in Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0001-8708","issn-type":"print"},{"key":"9","isbn-type":"print","first-page":"251","article-title":"Finite fields and their applications","author":"Niederreiter, Harald","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/3209013802"},{"key":"10","doi-asserted-by":"crossref","unstructured":"\\bysame, Nonlinear methods for pseudorandom number and vector generation, Simulation and Optimization (G. Pflug and U. Dieter, eds.), Lecture Notes in Econom. and Math. Systems, vol. 374, Springer, Berlin, 1992, pp. 145\u2013153.","DOI":"10.1007\/978-3-642-48914-3_11"},{"key":"11","isbn-type":"print","first-page":"375","article-title":"Finite fields, pseudorandom numbers, and quasirandom points","author":"Niederreiter, Harald","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/0824788052"},{"key":"12","series-title":"CBMS-NSF Regional Conference Series in Applied Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970081","volume-title":"Random number generation and quasi-Monte Carlo methods","volume":"63","author":"Niederreiter, Harald","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/0898712955"},{"key":"13","unstructured":"\\bysame, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech. 73 (1993), T648-T652."},{"key":"14","doi-asserted-by":"crossref","unstructured":"\\bysame, Pseudorandom vector generation by the inversive method, ACM Trans. Modeling and Computer Simulation 4 (1994), 191\u2013212.","DOI":"10.1145\/175007.175015"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1996-65-214\/S0025-5718-96-00706-5\/S0025-5718-96-00706-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-214\/S0025-5718-96-00706-5\/S0025-5718-96-00706-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:07:22Z","timestamp":1776719242000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-214\/S0025-5718-96-00706-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996]]},"references-count":14,"journal-issue":{"issue":"214","published-print":{"date-parts":[[1996,4]]}},"alternative-id":["S0025-5718-96-00706-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-96-00706-5","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1996]]}}}