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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6,1942-1960], we developed an incremental approach to compute the properorthogonal decomposition (POD) of PDE simulation data. Specifically, wedeveloped an incremental algorithm for the SVD with respect to a weighted innerproduct for the discrete time POD computations. For continuous time data, weused an approximate approach to arrive at a discrete time POD problem and thenapplied the incremental SVD algorithm. In this note, we analyze the continuoustime case with simulation data that is piecewise constant in time such thateach data snapshot is expanded in a finite collection of basis elements of aHilbert space. We first show that the POD is determined by the SVD of twodifferent data matrices with respect to weighted inner products. Next, wedevelop incremental algorithms for approximating the two matrix SVDs withrespect to the different weighted inner products. Finally, we show neitherapproximate SVD is more accurate than the other; specifically, we show theincremental algorithms return equivalent results.

A note on incremental POD algorithms for continuous time data