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Due to the versatility as well as its ease of implementation, the Fast Transversal Filters algorithm is attractive for many adaptive filtering applications. However, it is not widely used because of its undesirable tendency to diverge when operating in finite precision arithmetic. To compensate, modifications to the algorithm have been introduced that are either occasional (performed when a predefined condition(s) is violated) or structured as part of the normal update iteration. However, in neither...
With the emergence of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes for solving linear systems have recently been developed. However, in certain settings, GMRES may require too many iterations per refinement step, making it potentially more expensive than the alternative of recomputing the LU factors in a higher precision. In this work, we incorporate the idea of Krylov subspace recycling, a well-known technique for reusing information across sequential invocations,...
Numerical integration is an important operation for scientific computations.
Although the different quadrature methods have been well studied from a
mathematical point of view, the analysis of the actual error when performing
the quadrature on a computer is often neglected. This step is however required
for certified arithmetics.
We study the Newton-Cotes quadrature scheme in the context of
multiple-precision arithmetic and give enough details on the
algorithms and the error bounds to enable software...
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