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

Rational Krylov subspace projection methods are one of successful methods inMOR, mainly because some order derivatives of the approximate and originaltransfer functions are the same. This is the well known moments matchingresult. However, the properties of points which are far from the interpolatingpoints are little known. In this paper, we obtain the error's explicitexpression which involves shifts and Ritz values. The advantage of our resultover than the known moments matches theory is, to some extent, similar to theone of Lagrange type remainder formula over than Peano Type remainder formulain Taylor theorem. Expect for the proof, we also provide three explanations forthe error formula. One explanation shows that in the Gauss-Christoffelquadrature sense, the error is the Gauss quadrature remainder, when the Gaussquadrature formula is applied onto the resolvent function. By using the errorformula, we propose some greedy algorithms for the interpolatory $H_{\infty}$norm MOR.

Transfer function interpolation remainder formula of rational Krylov subspace methods