621 research outputs found
Generalizations of Weighted Trapezoidal Inequality for Monotonic Mappings and Its Applications
In this paper, we establish some generalizations of weighted trapezoid inequality for monotonic mappings, and give several applications for r − moment, the expectation of a continuous random variable and the Beta mapping
Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver
The FEAST method for solving large sparse eigenproblems is equivalent to
subspace iteration with an approximate spectral projector and implicit
orthogonalization. This relation allows to characterize the convergence of this
method in terms of the error of a certain rational approximant to an indicator
function. We propose improved rational approximants leading to FEAST variants
with faster convergence, in particular, when using rational approximants based
on the work of Zolotarev. Numerical experiments demonstrate the possible
computational savings especially for pencils whose eigenvalues are not well
separated and when the dimension of the search space is only slightly larger
than the number of wanted eigenvalues. The new approach improves both
convergence robustness and load balancing when FEAST runs on multiple search
intervals in parallel.Comment: 22 pages, 8 figure
Mercer–Trapezoid Rule for the Riemann–Stieltjes Integral with Applications
In this paper several new error bounds for the Mercer - Trapezoid quadrature rule for the Riemann-Stieltjes integral under various assumptions are proved. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well
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