A total positivity property of the Marchenko-Pastur Law

2015 ◽  
Vol 30 ◽  
Author(s):  
Ana Marco ◽  
Jose-Javier Martinez
Keyword(s):  
Orthogonal Polynomials ◽  
Gaussian Quadrature ◽  
Total Positivity ◽  
Quadrature Formulas ◽  
Positivity Property ◽  
Accurate Computation ◽  
Gaussian Quadrature Formulas ◽  
Theoretical Results

A property of the Marchenko-Pastur measure related to total positivity is presented. The theoretical results are applied to the accurate computation of the roots of the corresponding orthogonal polynomials, an important issue in the construction of Gaussian quadrature formulas.

Padé approximation and orthogonal polynomials

1974 ◽  
Vol 10 (2) ◽  
pp. 263-270 ◽  
Author(s):  
G.D. Allen ◽  
C.K. Chui ◽  
W.R. Madych ◽  
F.J. Narcowich ◽  
P.W. Smith
Keyword(s):  
Power Series ◽  
Variational Method ◽  
Orthogonal Polynomials ◽  
Gaussian Quadrature ◽  
Quadrature Formulas ◽  
The Past ◽  
Gaussian Quadrature Formulas ◽  
Poles And Zeros ◽  
Formal Power ◽  
Determinant Theory

By using a variational method, we study the structure of the Padé table for a formal power series. For series of Stieltjes, this method is employed to study the relations of the Padé approximants with orthogonal polynomials and gaussian quadrature formulas. Hence, we can study convergence, precise locations of poles and zeros, monotonicity, and so on, of these approximants. Our methods have nothing to do with determinant theory and the theory of continued fractions which were used extensively in the past.

Sign in / Sign up

Export Citation Format

Share Document