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

This report shows on real data that the direct methods such as LDLdecomposition and Gaussian elimination for solving linear systems withill-conditioned matrices provide inaccurate results due to divisions by verysmall numbers, which in turn results in peaking phenomena and large estimationerrors. Richardson iteration provides accurate results without peakingphenomena since division by small numbers is absent in the Richardson approach.In addition, two preconditioners are considered and compared in the Richardsoniteration: 1) the simplest and robust preconditioner based on the maximum rowsum matrix norm and 2) the optimal one based on calculation of the eigenvalues.It is shown that the simplest preconditioner is more robust for ill-conditionedcase and therefore it is recommended for many applications.

Richardson Approach or Direct Methods? What to Apply in the Ill-Conditioned Least Squares Problem