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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 5
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Articles

Small perturbations of polynomial meshes

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Pages 1063-1073 | Received 24 Apr 2011, Accepted 11 Dec 2011, Published online: 18 Jan 2012

References

  • Calvi , JP and Levenberg , N . 2008 . Uniform approximation by discrete least squares polynomials . J. Approx. Theory , 152 : 82 – 100 .
  • Jetter , K , Stöckler , J and Ward , JD . 1999 . Norming Sets and Spherical Cubature Formulas, Lecture Notes in Pure and Applied Mathematics Vol. 202 , 237 – 244 . Dekker, New York
  • Marzo , J . 2007 . Marcinkiewicz–Zygmund inequalities and interpolation by spherical harmonics . J. Funct. Anal. , 250 : 559 – 587 .
  • Rieger , C , Schaback , R and Zwicknagl , B . 2010 . Sampling and Stability, Lecture Notes in Computer Science , Vol. 5862 , 347 – 369 . Berlin : Springer .
  • Bos , L , De Marchi , S , Sommariva , A and Vianello , M . 2010 . Computing multivariate Fekete and Leja points by numerical linear algebra . SIAM J. Numer. Anal. , 48 : 1984 – 1999 .
  • Bos , L and Levenberg , N . 2008 . On the approximate calculation of Fekete points: The univariate case . Electron. Trans. Numer. Anal. , 30 : 377 – 397 .
  • Sommariva , A and Vianello , M . 2009 . Computing approximate Fekete points by QR factorizations of Vandermonde matrices . Comput. Math. Appl. , 57 : 1324 – 1336 .
  • Berman , R , Boucksom , S and Witt Nyström , D . 2011 . Fekete points and convergence towards equilibrium measures on complex manifolds . Acta Math. , 207 : 1 – 27 .
  • Klimek , M . 1991 . Pluripotential Theory , New York : Oxford University Press .
  • Kroó , A . 2003 . “ Classical polynomial inequalities in several variables ” . In Constructive Theory of Functions Edited by: Bojanov , B . 19 – 32 . Darba, Sofia
  • Bos , L , Sommariva , A and Vianello , M . 2010 . Least-squares polynomial approximation on weakly admissible meshes: Disk and triangle . J. Comput. Appl. Math. , 235 : 660 – 668 .
  • Bos , L and Vianello , M . 2012 . Low cardinality admissible meshes on quadrangles, triangles and disks . Math. Inequal. Appl. , 15 : 229 – 235 .
  • Kroó , A . 2011 . On optimal polynomial meshes . J. Approx. Theory , 163 : 1107 – 1124 .
  • Piazzon , F and Vianello , M . 2010 . Analytic transformations of admissible meshes . East J. Approx. , 16 : 316 – 322 .
  • Rockafellar , RT and Wets , RJ-B . 1998 . Variational Analysis , Berlin : Springer .
  • Brutman , L . 1997 . Lebesgue functions for polynomial interpolation—A survey . Ann. Numer. Math. , 4 : 111 – 127 .
  • Boyd , JP and Xu , F . 2009 . Divergence (Runge phenomenon) for least-squares polynomial approximation on an equispaced grid and Mock-Chebyshev subset interpolation . Appl. Math. Comput. , 210 : 158 – 168 .
  • Bos , L , Caliari , M , De Marchi , S , Vianello , M and Xu , Y . 2006 . Bivariate Lagrange interpolation at the Padua points: The generating curve approach . J. Approx. Theory , 143 : 15 – 25 .
  • Newman , DJ and Shapiro , HS . 1964 . “ Jackson's Theorem in Higher Dimension ” . In Proceedings Conference on Approximation Theory (Oberwolfach, 1963) , 208 – 219 . Basel : Birkhäuser .
  • Ragozin , DL . 1971 . Constructive polynomial approximation on spheres and projective spaces . Trans. Am. Math. Soc. , 162 : 157 – 170 .
  • Bagby , T , Bos , L and Levenberg , N . 2002 . Multivariate simultaneous approximation . Constr. Approx. , 18 : 569 – 577 .
  • Pleśniak , W . 2009 . Multivariate Jackson inequality . J. Comput. Appl. Math. , 233 : 815 – 820 .
  • Levenberg , N . 2006 . Approximation in ℂ N . Surv. Approx. Theory , 2 : 92 – 140 .
  • Pommerenke , C . 1959 . On the derivative of a polynomial . Mich. Math. J. , 6 : 373 – 375 .
  • Białas-Cież , L and Calvi , J-P . 2012 . Pseudo Leja sequences . Ann. Mat. Pura Appl. , 191 : 53 – 75 .
  • Grisvard , P . 1985 . Elliptic Problems in Nonsmooth Domains Pitman, Boston
  • Krantz , SG . 2006 . Geometric Function Theory , Boston : Birkhäuser .
  • Andersson , A . 2009 . Modified Schwarz-Christoffel mappings using approximate curves factors . J. Comput. Appl. Math. , 233 : 1117 – 1127 .

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