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Interval arithmetic normally deals with intervals defined as $[a,b]$ with rules like $$[a,b]+[c,d]=[a+c,b+d]$$ I am interested in interval arithmetic with different interval definitions such as $$\{a\}...

The Euler--MacLaurin summation formula can be written as $$ \sum_{i=0}^{n-1} f(k)\approx \int^{n-1}_0f(x)\,dx + \frac{f(n-1) + f(0)}2 + \sum_{j=1}^m\frac{B_{2j}}{(2j)!}[f^{(2j - 1)}(n-1)...

tl;dr: Are there explicit bounds for the approximation error by orthogonal polynomials? There are various ways to formulate this question more precisely, so want I emphasize up front that this is a ...

Is there any proof for this. Kindly request a reference in case available or any related documents towards this. PS : I am specifically interested in the case of scattered data (irregularly placed), ...

I'm working on a project and think that matrices and vectors of intervals will be useful. I'm aware about interval arithmetic, but there is little information on the internet, regarding matrices and ...