Abstract
AbstractThis work studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space $L_{2}^{(m)}(0,1)$
L
2
(
m
)
(
0
,
1
)
for numerical calculation of Fourier coefficients. Using Sobolev’s method, we obtain new sine and cosine weighted optimal quadrature formulas of such type for $N + 1\geq m$
N
+
1
≥
m
, where $N + 1$
N
+
1
is the number of nodes. Then, explicit formulas for the optimal coefficients of optimal quadrature formulas are obtained. The obtained optimal quadrature formulas in $L_{2}^{(m)}(0,1)$
L
2
(
m
)
(
0
,
1
)
space are exact for algebraic polynomials of degree $(m-1)$
(
m
−
1
)
.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference23 articles.
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