Ray Sequences of Best Rational Approximants For |x|α
1997 ◽
Vol 49
(5)
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pp. 1034-1065
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Keyword(s):
AbstractThe convergence behavior of best uniform rational approximations with numerator degree m and denominator degree n to the function |x|α, α > 0, on [-1, 1] is investigated. It is assumed that the indices (m, n) progress along a ray sequence in the lower triangle of the Walsh table, i.e. the sequence of indices {(m, n)} satisfiesIn addition to the convergence behavior, the asymptotic distribution of poles and zeros of the approximants and the distribution of the extreme points of the error function on [-1, 1] will be studied. The results will be compared with those for paradiagonal sequences (m = n + 2[α/2]) and for sequences of best polynomial approximants.
1979 ◽
Vol 31
(1)
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pp. 9-16
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Keyword(s):
1969 ◽
Vol 16
(3)
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pp. 245-250
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1995 ◽
Vol 47
(6)
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pp. 1121-1147
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1985 ◽
Vol 101
(1-2)
◽
pp. 99-110
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1976 ◽
Vol 10
(2)
◽
pp. 475-478
2001 ◽
Vol 108
(1)
◽
pp. 53-96
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