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

This paper presents an efficient method to perform Structured MatrixApproximation by Separation and Hierarchy (SMASH), when the original densematrix is associated with a kernel function. Given points in a domain, a treestructure is first constructed based on an adaptive partitioning of thecomputational domain to facilitate subsequent approximation procedures. Incontrast to existing schemes based on either analytic or purely algebraicapproximations, SMASH takes advantage of both approaches and greatly improvesthe efficiency. The algorithm follows a bottom-up traversal of the tree and isable to perform the operations associated with each node on the same level inparallel. A strong rank-revealing factorization is applied to the initialanalytic approximation in the separation regime so that a special structure isincorporated into the final nested bases. As a consequence, the storage issignificantly reduced on one hand and a hierarchy of the original grid isconstructed on the other hand. Due to this hierarchy, nested bases at upperlevels can be computed in a similar way as the leaf level operations but oncoarser grids. The main advantages of SMASH include its simplicity ofimplementation, its flexibility to construct various hierarchical rankstructures and a low storage cost. Rigorous error analysis and complexityanalysis are conducted to show that this scheme is fast and stable. Theefficiency and robustness of SMASH are demonstrated through various testproblems arising from integral equations, structured matrices, etc.

SMASH: Structured matrix approximation by separation and hierarchy