Rational approximations to fractional powers of self-adjoint positive operators
arXiv:1807.1008629 citationsh-index: 20
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Provides tighter theoretical error bounds for rational approximations of operator functions, relevant to numerical analysis and scientific computing.
The paper improves error bounds for rational approximations of fractional powers of unbounded positive operators using Padé approximants, with numerical experiments confirming accuracy.
We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in approximation theory involving Padé approximants. The analysis improves some existing results and the numerical experiments proves its accuracy.