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Let $I = [0,1]$ be the unit interval Let $I$ be partioned into $n$ closed subintervals $(I_j)_J$, each of length $1/n$. Let $X_{DC} = \{ v \in L^2[0,1] | 1 \leq j \leq n : v_{|I_j} \in \mathcal P_1( …

Consider the Newton iteration $x^{(k+1)} = x^{(k)} - DF( x^{(k)} )^{-1} \cdot F( x^{(k)} )$ to find a zero of a function $F : \mathbb R^k \rightarrow \mathbb R^k$. If we freeze the first derivative …

The Sobolev gradient concept has been developed in the 1970s, with a first publication in 1985, and an introduction can be found at: Ranka I would like to learn how strong the impact of Sobolev gradi …

Before the proliferation of computers in the 1950s, did human computers use floating-point formats for their computations? Floating-point calculation was reportedly implemented already in the 1910s (W …

Hello, in contrast to the more discrete part of computational mathematics (cryptography, combinatorial computation), numerical mathematics seems to ignore typical questions of theoretical computer sc …

Hello, Regge calculus is an approximation scheme for General Relativity, which has been introduced in early-sixties and has been adopted both in numerical relativity and numerical quantum relativity. …

Hello, in numerical analysis, it is common to compare the behavior of different algorithms, and of different implementation of algorithms. This occurs not only on the theoretical level, but also on t …