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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this work, we consider two types of large-scale quadratic matrixequations: Continuous-time algebraic Riccati equations, which play a centralrole in optimal and robust control, and unilateral quadratic matrix equations,which arise from stochastic processes on 2D lattices and vibrating systems. Wepropose a simple and fast way to update the solution to such matrix equationsunder low-rank modifications of the coefficients. Based on this procedure, wedevelop a divide-and-conquer method for quadratic matrix equations withcoefficients that feature a specific type of hierarchical low-rank structure,which includes banded matrices. This generalizes earlier work on linear matrixequations. Numerical experiments indicate the advantages of our newly proposedmethod versus iterative schemes combined with hierarchical low-rank arithmetic.

Low-rank updates and divide-and-conquer methods for quadratic matrix equations