ISSN:
0945-3245
Keywords:
AMS (MOS): 65D32
;
41A17
;
CR: G 1.4
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary In this paper we consider product formulas of interpolatory type for the two-dimensional Cauchy principal value integral: $$I(f;\eta _1 ,\eta _2 ) = \int\limits_{ - 1}^1 {\int\limits_{ - 1}^1 \omega (x,y)\frac{{f(x,y)}}{{(x - \eta _1 )(y - \eta _2 )}}dxdy} $$ where: η1, η2∈(−1,1), ω(x,y)=ω1(x)·ω2(y), and ω1(x) and ω2(x) are two absolutely integrable weight functions. The integral is approximated by $$F_{n,m} (f;\eta _1 ,\eta _2 ) = \sum\limits_{i = 0}^n {\sum\limits_{j = 0}^m {A_i^{(1)} (\eta _1 )A_j^{(2)} (\eta _2 )} f(x_i ,y_i )}$$ where the nodes {x i } and {y j } are the zeros of the Chebyshev polynomials of the first kind, commonly named “classical” abscissas, or the Clenshaw points, often called “practical” abscissas. We present convergence results for these rules.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01400259
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