```000028619 001__ 28619
000028619 005__ 20150420164336.0
000028619 0248_ \$\$aoai:doc.rero.ch:20120229084549-BI\$\$punifr\$\$ppostprint\$\$prero_explore\$\$particle\$\$zthesis_urn\$\$zreport\$\$zthesis\$\$zbook\$\$zcdu51\$\$zjournal\$\$zcdu16\$\$zpreprint\$\$zcdu1\$\$zdissertation\$\$zcdu34
000028619 041__ \$\$aeng
000028619 080__ \$\$a51
000028619 100__ \$\$aKlein, Georges\$\$uDepartment of Mathematics, University of Fribourg, Switzerland
000028619 245__ \$\$9eng\$\$aLinear barycentric rational quadrature
000028619 269__ \$\$c2011-09-24
000028619 520__ \$\$9eng\$\$aLinear interpolation schemes very naturally lead to quadrature rules. Introduced in the eighties, linear barycentric rational interpolation has recently experienced a boost with the presentation of new weights by Floater and Hormann. The corresponding interpolants converge in principle with arbitrary high order of precision. In the present paper we employ them to construct two linear rational quadrature rules. The weights of the first are obtained through the direct numerical integration of the Lagrange fundamental rational functions; the other rule, based on the solution of a simple boundary value problem, yields an approximation of an antiderivative of the integrand.The convergence order in the first case is shown to be one unit larger than that of the interpolation, under some restrictions. We demonstrate the efficiency of both approaches with numerical tests.
000028619 695__ \$\$9eng\$\$aRational interpolation ; barycentric form ; quadrature
000028619 700__ \$\$aBerrut, Jean-Paul\$\$uDepartment of Mathematics, University of Fribourg, Switzerland
000028619 773__ \$\$g2012/52/2/407-424\$\$tBit Numerical Mathematics
000028619 775__ \$\$gPublished version\$\$ohttp://dx.doi.org/10.1007/s10543-011-0357-x
000028619 8564_ \$\$fkle_lbr.pdf\$\$qapplication/pdf\$\$s237533\$\$uhttp://doc.rero.ch/record/28619/files/kle_lbr.pdf\$\$yorder:1\$\$zpdf
000028619 918__ \$\$aFaculté des sciences\$\$bDécanat, Ch. du Musée 6A, 1700 Fribourg\$\$cMathématiques
000028619 919__ \$\$aUniversité de Fribourg\$\$bFribourg\$\$ddoc.support@rero.ch
000028619 980__ \$\$aPOSTPRINT\$\$bUNIFR\$\$fART_JOURNAL
000028619 990__ \$\$a20120229084549-BI```