Quasi-symmetric orthogonal polynomials on the real line: moments, quadrature rules and invariance under Christoffel modifications
Given a , b ∈ R , m = min { a , b } and M = max { a , b } , we consider the orthogonal polynomials associated with nontrivial positive measures ϕ for which s u p p ( ϕ ) ⊂ ( - ∞ , m ] ∪ [ M , ∞ ) and ( x - a ) d ϕ ( x ) = - ( x - b ) d ϕ ( - x + a + b ) . For this class of measures, formulas in orde...
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| Vydané v: | Computational & applied mathematics Ročník 42; číslo 3 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Cham
Springer International Publishing
01.04.2023
|
| Predmet: | |
| ISSN: | 2238-3603, 1807-0302 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | Given
a
,
b
∈
R
,
m
=
min
{
a
,
b
}
and
M
=
max
{
a
,
b
}
,
we consider the orthogonal polynomials associated with nontrivial positive measures
ϕ
for which
s
u
p
p
(
ϕ
)
⊂
(
-
∞
,
m
]
∪
[
M
,
∞
)
and
(
x
-
a
)
d
ϕ
(
x
)
=
-
(
x
-
b
)
d
ϕ
(
-
x
+
a
+
b
)
.
For this class of measures, formulas in order to compute the moments, as well as formulas for the weights and nodes in the associated Gaussian quadrature rules are provided. We also show that the QD-algorithm can be applied in order to generate new orthogonal polynomials in a simple way. Several examples are given to illustrate the results obtained. |
|---|---|
| ISSN: | 2238-3603 1807-0302 |
| DOI: | 10.1007/s40314-023-02276-z |