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  • 12 votes cast
Jan
2
comment Claimed Quadrature Results seem Impossible
we have uploaded a new version (in the above github link) and will go to arxiv soon. we have paid a lot of attention to your remarks and in fact we do not rely on the firstly mentioned results but on numerous other results that were published in peer-reviewed papers. we also did not forget to acknowledge you in the paper. thanks again!
Jan
2
revised Claimed Quadrature Results seem Impossible
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Dec
31
revised Claimed Quadrature Results seem Impossible
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Dec
29
revised Claimed Quadrature Results seem Impossible
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Dec
28
revised Claimed Quadrature Results seem Impossible
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Dec
28
revised Claimed Quadrature Results seem Impossible
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Dec
28
comment Claimed Quadrature Results seem Impossible
Right, the Fourier analysis would suggest points that'll keep it outside of P, as can be seen by translating the product of n cosines into sum of 2^n cosines. This is definitely part of why it is all so confusing. But the paper suggests a calculation for the number of points needed, including the precision needed, and it all seems P.
Dec
28
comment Claimed Quadrature Results seem Impossible
Indeed, just finished writing a proof for that :) Just uploaded updated pdf to github. It's all still preliminary though.
Dec
27
comment Claimed Quadrature Results seem Impossible
thanks, all your comments will be taken into account in the new revision that will be published tomorrow. We do think we can show that the result still holds, even in more general cases. In fact we derived a new proof without O() at all.
Dec
27
revised Claimed Quadrature Results seem Impossible
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Dec
27
revised Claimed Quadrature Results seem Impossible
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Dec
26
revised Claimed Quadrature Results seem Impossible
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Dec
26
revised Claimed Quadrature Results seem Impossible
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Dec
26
comment Claimed Quadrature Results seem Impossible
after your edit: yes, indeed, disturbing questions - and indeed we claim that the quadrature rates are too optimistic. alas, they are proved both theoretically and experimentally. we can't point to an error yet.
Dec
26
comment Claimed Quadrature Results seem Impossible
right, and indeed, the constant are independent of the integrand, as stated in the Borwein&Ye paper where the theorem was taken from. will make it clear. thanks!
Dec
26
asked Claimed Quadrature Results seem Impossible
Sep
7
awarded  Popular Question
Sep
24
awarded  Autobiographer
Jan
12
comment RFC for definite integral connection to second derivative
Thanks Gerald I appreciate your help
Jan
12
accepted RFC for definite integral connection to second derivative