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/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A novel algorithm for computing the action of a matrix exponential over avector is proposed. The algorithm is based on a multilevel Monte Carlo method,and the vector solution is computed probabilistically generating suitablerandom paths which evolve through the indices of the matrix according to asuitable probability law. The computational complexity is proved in this paperto be significantly better than the classical Monte Carlo method, which allowsthe computation of much more accurate solutions. Furthermore, the positivefeatures of the algorithm in terms of parallelism were exploited in practice todevelop a highly scalable implementation capable of solving some test problemsvery efficiently using high performance supercomputers equipped with a largenumber of cores. For the specific case of shared memory architectures theperformance of the algorithm was compared with the results obtained using anavailable Krylov-based algorithm, outperforming the latter in all benchmarksanalyzed so far.

A highly parallel algorithm for computing the action of a matrix exponential on a vector based on a multilevel Monte Carlo method