18 research outputs found
AAA rational approximation on a continuum
AAA rational approximation has normally been carried out on a discrete set,
typically hundreds or thousands of points in a real interval or complex domain.
Here we introduce a continuum AAA algorithm that discretizes a domain
adaptively as it goes. This enables fast computation of high-accuracy rational
approximations on domains such as the unit interval, the unit circle, and the
imaginary axis, even in some cases where resolution of singularities requires
exponentially clustered sample points, support points, and poles. Prototype
MATLAB (or Octave) and Julia codes aaax, aaaz, and aaai are provided for these
three special domains; the latter two are equivalent by a Moebius
transformation. Execution is very fast since the matrices whose SVDs are
computed have only three times as many rows as columns. The codes include a
AAA-Lawson option for improvement of a AAA approximant to minimax, so long as
the accuracy is well above machine precision. The result returned is pole-free
in the approximation domain
Investigation into the dehydration of selenate doped Na2M(SO4)2·2H2O (M = Mn, Fe, Co and Ni): Stabilisation of the high Na content alluaudite phases Na3M1.5(SO4)3-1.5x(SeO4)1.5x (M = Mn, Co and Ni) through selenate incorporation
Mechanically evoked sensory and motor responses to dynamic compression of the ulnar nerve
Charge transport by polyatomic anion diffusion in Sc2(WO 4)3
10.1021/cm800466yChemistry of Materials20206335-6345CMAT