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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

An improved preconditioned conjugate gradient squared (PCGS) algorithm hasrecently been proposed, and it performs much better than the conventional PCGSalgorithm. In this paper, the improved PCGS algorithm is verified as acoordinative to the left-preconditioned system, and it has the advantages ofboth the conventional and the left-PCGS; this is done by comparing, analyzing,and executing numerical examinations of various PCGS algorithms, includinganother improved one. We show that the direction of the preconditioned systemfor the CGS method is determined by the operations of $\alpha_k$ and $\beta_k$in the PCGS algorithm. By comparing the logical structures of these algorithms,we show that the direction of the preconditioned system can be switched by theconstruction and setting of the initial shadow residual vector.

Structure of the preconditioned system in various preconditioned conjugate gradient squared algorithms