Nearest neighbor recurrence relations for multiple orthogonal polynomials

Nearest neighbor recurrence relations for Multiple Orthogonal Polynomials; Recursierelaties voor nabije buren van meervoudig orthogonale veeltermen

We show that multiple orthogonal polynomials for r measures (μ1, . . . , μr) satisfy a system of linear recurrence relations only involving nearest neighbor multi-indices ~n ± ~ej, where ~ej are the standard unit vectors. The recurrence coefficients are not arbitrary but satisfy a system of partial difference equations with boundary values given by the recurrence coefficients of the orthogonal ...

Asymptotics of Orthogonal Polynomials via Recurrence Relations

Recurrence Relations for Orthogonal Polynomials on Triangular Domains

Abstract: In Farouki et al, 2003, Legendre-weighted orthogonal polynomials Pn,r(u, v, w), r = 0, 1, . . . , n, n ≥ 0 on the triangular domain T = {(u, v, w) : u, v, w ≥ 0, u+ v+w = 1} are constructed, where u, v, w are the barycentric coordinates. Unfortunately, evaluating the explicit formulas requires many operations and is not very practical from an algorithmic point of view. Hence, there is...

An Algorithm for Predicting Recurrence of Breast Cancer Using Genetic Algorithm and Nearest Neighbor Algorithm

Introduction: Breast cancer is one of the most common types of cancer and the most common type of malignancy in women, which has been growing in recent years. Patients with this disease have a chance of recurrence. Many factors reduce or increase this probability. Data mining is one of the methods used to detect or anticipate cancers, and one of its most common uses is to predict the recurrence...

An Algorithm for Predicting Recurrence of Breast Cancer Using Genetic Algorithm and Nearest Neighbor Algorithm

Introduction: Breast cancer is one of the most common types of cancer and the most common type of malignancy in women, which has been growing in recent years. Patients with this disease have a chance of recurrence. Many factors reduce or increase this probability. Data mining is one of the methods used to detect or anticipate cancers, and one of its most common uses is to predict the recurrence...