English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We consider the computation of the matrix logarithm by using numericalquadrature. The efficiency of numerical quadrature depends on the integrand andthe choice of quadrature formula. The Gauss--Legendre quadrature has beenconventionally employed; however, the convergence could be slow forill-conditioned matrices. This effect may stem from the rapid change of theintegrand values. To avoid such situations, we focus on the double exponentialformula, which has been developed to address integrands with endpointsingularity. In order to utilize the double exponential formula, we mustdetermine a suitable finite integration interval, which provides the requiredaccuracy and efficiency. In this paper, we present a method for selecting asuitable finite interval based on an error analysis as well as two algorithms,and one of these algorithms addresses error control.

Algorithms for the computation of the matrix logarithm based on the double exponential formula