Gauss quadrature for quasi-definite linear functionals

2016 ◽  
pp. dnw032 ◽  
Author(s):  
Stefano Pozza ◽  
Miroslav S. Pranić ◽  
Zdeněk Strakoš
Keyword(s):  
Gauss Quadrature ◽  
Linear Functionals

scholarly journals Complex Jacobi Matrices and Gauss Quadrature for Quasi-definite Linear Functionals

2015 ◽  
Author(s):  
Stefano Pozza ◽  
Miroslav Pranić ◽  
Zdenek Strakoš
Keyword(s):  
Orthogonal Polynomials ◽  
Positive Definite ◽  
Gauss Quadrature ◽  
Jacobi Matrices ◽  
Linear Functionals ◽  
Underlying Theory ◽  
Close Relationship

The Gauss quadrature can be formulated as a method for approximation of positive definite linear functionals. The underlying theory connects several classical topics including orthogonal polynomials and (real) Jacobi matrices. In the poster we investigated the problem of generalizing the concept of Gauss quadrature for approximation of linear functionals which are not positive definite. We showed that the concept can be generalized to quasi-definite functionals and based on a close relationship with orthogonal polynomials and complex Jacobi matrices.

Bounded Linear Functionals on L q

1965 ◽  
Vol 72 (7) ◽  
pp. 750
Author(s):  
W. Fulks
Keyword(s):  
Linear Functionals ◽  
Bounded Linear

scholarly journals The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type

2020 ◽  
Vol 369 ◽  
pp. 124806
Author(s):  
Ramón Orive ◽  
Aleksandar V. Pejčev ◽  
Miodrag M. Spalević
Keyword(s):  
Error Bounds ◽  
Gauss Quadrature ◽  
Weight Functions ◽  
Quadrature Formulae

scholarly journals Spectral Transformations and Associated Linear Functionals of the First Kind

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 107
Author(s):  
Juan Carlos García-Ardila ◽  
Francisco Marcellán
Keyword(s):  
Orthogonal Polynomials ◽  
Linear Space ◽  
Linear Functional ◽  
Linear Functionals ◽  
Spectral Transformations ◽  
Christoffel Transformation ◽  
Complex Coefficients

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For a canonical Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0, and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.

Measurement of Wiener kernels

1984 ◽  
Vol 16 (1) ◽  
pp. 11-12
Author(s):  
Yoshifusa Ito
Keyword(s):  
Differential Operator ◽  
Mathematical Models ◽  
White Noise ◽  
Linear Systems ◽  
Main Part ◽  
The Other ◽  
Linear Functionals ◽  
Wiener Kernels ◽  
Non Linear ◽  
Non Linear Systems

Since the late 1960s Wiener's theory on the non-linear functionals of white noise has been widely applied to the construction of mathematical models of non-linear systems, especially in the field of biology. For such applications the main part is the measurement of Wiener's kernels, for which two methods have been proposed: one by Wiener himself and the other by Lee and Schetzen. The aim of this paper is to show that there is another method based on Hida's differential operator.

Extrema of linear functionals on finite-dimensional spaces

2000 ◽  
Vol 55 (6) ◽  
pp. 1143-1145
Author(s):  
V B Demidovich ◽  
G G Magaril-Il'yaev ◽  
V M Tikhomirov
Keyword(s):  
Linear Functionals ◽  
Finite Dimensional
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