{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:54:43Z","timestamp":1776722083549,"version":"3.51.2"},"reference-count":31,"publisher":"American Mathematical Society (AMS)","issue":"218","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"

\n Let\n \n \n \n f<\/mml:mi>\n f<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n be an entire function of positive order and finite type. The subject of this note is the convergence acceleration of polynomial approximants of\n \n \n \n f<\/mml:mi>\n f<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n by incorporating information about the growth of\n \n \n \n \n f<\/mml:mi>\n (<\/mml:mo>\n z<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n f(z)<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n for\n \n \n \n \n z<\/mml:mi>\n \n \u2192\n \n <\/mml:mo>\n \n \u221e\n \n <\/mml:mi>\n <\/mml:mrow>\n z\\to \\infty<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n . We consider \u201cnear polynomial approximation\u201d on a compact plane set\n \n \n \n K<\/mml:mi>\n K<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n , which should be thought of as a circle or a real interval. Our aim is to find sequences\n \n \n \n \n (<\/mml:mo>\n \n f<\/mml:mi>\n n<\/mml:mi>\n <\/mml:msub>\n \n )<\/mml:mo>\n n<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n (f_n)_n<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n of functions which are the product of a polynomial of degree\n \n \n \n \n \n \u2264\n \n <\/mml:mo>\n n<\/mml:mi>\n <\/mml:mrow>\n \\le n<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n and an \u201ceasy computable\u201d second factor and such that\n \n \n \n \n (<\/mml:mo>\n \n f<\/mml:mi>\n n<\/mml:mi>\n <\/mml:msub>\n \n )<\/mml:mo>\n n<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n (f_n)_n<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n converges essentially faster to\n \n \n \n f<\/mml:mi>\n f<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n on\n \n \n \n K<\/mml:mi>\n K<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n than the sequence\n \n \n \n \n (<\/mml:mo>\n \n P<\/mml:mi>\n n<\/mml:mi>\n \n \u2217\n \n <\/mml:mo>\n <\/mml:msubsup>\n \n )<\/mml:mo>\n n<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n (P_n^*)_n<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n of best approximating polynomials of degree\n \n \n \n \n \n \u2264\n \n <\/mml:mo>\n n<\/mml:mi>\n <\/mml:mrow>\n \\le n<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n . The resulting method, which we call Reduced Growth method (\n \n \n \n \n R<\/mml:mi>\n G<\/mml:mi>\n <\/mml:mrow>\n RG<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -method) is introduced in Section\u00a02. In Section\u00a05, numerical examples of the\n \n \n \n \n R<\/mml:mi>\n G<\/mml:mi>\n <\/mml:mrow>\n RG<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -method applied to the complex error function and to Bessel functions are given.\n <\/p>","DOI":"10.1090\/s0025-5718-97-00832-6","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:13:53Z","timestamp":1027707233000},"page":"743-761","source":"Crossref","is-referenced-by-count":5,"title":["Accelerated polynomial approximation of finite order entire functions by growth reduction"],"prefix":"10.1090","volume":"66","author":[{"given":"J\u00fcrgen","family":"M\u00fcller","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1997]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"Amos, D.E., A portable package for Bessel functions of a complex argument and nonnegative order, ACM Trans. Math. 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