from general to rectangular sets of nodes M. Crainic and N. Crainic Received: June 24, 2008; Revised: March 20, 2009; Accepted: March 30, 2009 Abstract. Polya conditions are certain algebraic inequalities that regular Birkhoff interpolation schemes must satisfy, and they are useful in deciding if a given scheme is regular or not. Here we review the classical Polya condition and then we show how it can be strengthened in the case of rectangular nodes. Keywords: Birkhoff interpolation, multivariate interpolation, Polya. AMS Subject classification: Primary: 65D055, 41A63. Version to read: PDF ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |