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

Projection methods provide an appealing way to construct reduced-order modelsof large-scale linear dynamical systems: they are intuitively motivated andfairly easy to compute. Unfortunately, the resulting reduced models need notinherit the stability of the original system. How many unstable modes can thesereduced models have? This note investigates this question, using theoryoriginally motivated by iterative methods for linear algebraic systems andeigenvalue problems, and illustrating the theory with a number of smallexamples. From these results follow rigorous upper bounds on the number ofunstable modes in reduced models generated via orthogonal projection, for bothcontinuous- and discrete-time systems. Can anything be learned from theunstable modes in reduced-order models? Several examples illustrate how suchinstability can helpfully signal transient growth in the original system.

Unstable modes in projection-based reduced-order models: How many can there be, and what do they tell you?