Orthogonal and Similar Polynomials with some analytical and numerical applications

• Grant number: 14/22571-2
• Support Opportunities: Regular Research Grants
• Start date: February 01, 2015
• End date: January 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cleonice Fátima Bracciali
• Grantee: Cleonice Fátima Bracciali
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

Abstract

This project deals with topics related to orthogonal polynomials and polynomials and functions that have similar characteristics to the orthogonal polynomials. It is well known that the coefficients of the three term recurrence relations satisfied by certain orthogonal polynomials are solutions of systems of equation which are integrable systems. In this project we intended to investigate the properties of the coefficients of the recurrence relations of orthogonal L-polynomials in a similar way, and also to investigate extension of this theory for the case of orthogonal polynomials in two variables. Another subject of investigation will be the relationship between the theory of discrete orthogonal polynomials in several variables and some numerical methods such as the fast multipole method that requires numerical calculation of integrals, and meshless methods for numerical solution of partial differential equations. Furthermore, for some bi-orthogonal functions that satisfy a three term recurrence relation, we will investigate their asymptotic behavior and the behavior of their zeros. (AU)

Scientific publications

(7)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BRACCIALI, CLEONICE F.; SILVA, JAIRO S.; RANGA, A. SRI; VERONESE, DANIEL O.. Orthogonal polynomials on the unit circle: Verblunsky coefficients with some restrictions imposed on a pair of related real sequences. COMPUTATIONAL & APPLIED MATHEMATICS, v. 37, n. 2, p. 1142-1161, MAY 2018. (14/22571-2)

BRACCIALI, CLEONICE F.; PEREZ, TERESA E.. Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs. Applied Mathematics and Computation, v. 309, p. 142-155, SEP 15 2017. (14/22571-2)

BRACCIALI, CLEONICE F.; SILVA, JAIRO S.; RANGA, A. SRI. Explicit formulas for OPUC and POPUC associated with measures which are simple modifications of the Lebesgue measure. Applied Mathematics and Computation, v. 271, p. 820-831, NOV 15 2015. (14/22571-2, 09/13832-9)

BOTTA, VANESSA; BRACCIALI, CLEONICE F.; PEREIRA, JUNIOR A.. Some properties of classes of real self-reciprocal polynomials. Journal of Mathematical Analysis and Applications, v. 433, n. 2, p. 1290-1304, JAN 15 2016. (14/22571-2, 13/08012-8)

BRACCIALI, CLEONICE F.; CARLEY, MICHAEL. Quasi-analytical root-finding for non-polynomial functions. NUMERICAL ALGORITHMS, v. 76, n. 3, p. 639-653, NOV 2017. (14/22571-2, 14/17357-1)

BRACCIALI, CLEONICE F.; SILVA, JAIRO S.; SRI RANGA, A.; VERONESE, DANIEL O.. Verblunsky coefficients related with periodic real sequences and associated measures on the unit circle. Journal of Mathematical Analysis and Applications, v. 445, n. 1, p. 719-745, JAN 1 2017. (14/22571-2)

BRACCIALI, CLEONICE F.; SILVA, JAIRO S.; RANGA, A. SRI; VERONESE, DANIEL O.. Orthogonal polynomials on the unit circle: Verblunsky coefficients with some restrictions imposed on a pair of related real sequences. COMPUTATIONAL & APPLIED MATHEMATICS, v. 37, n. 2, p. 20-pg., 2018-05-01. (14/22571-2)