Transfer function interpolation remainder formula of rational Krylov subspace methods

02/23/2021
by   Yiding Lin, et al.
0

Rational Krylov subspace projection methods are one of successful methods in MOR, mainly because some order derivatives of the approximate and original transfer functions are the same. This is the well known moments matching result. However, the properties of points which are far from the interpolating points are little known. In this paper, we obtain the error's explicit expression which involves shifts and Ritz values. The advantage of our result over than the known moments matches theory is, to some extent, similar to the one of Lagrange type remainder formula over than Peano Type remainder formula in Taylor theorem. Expect for the proof, we also provide three explanations for the error formula. One explanation shows that in the Gauss-Christoffel quadrature sense, the error is the Gauss quadrature remainder, when the Gauss quadrature formula is applied onto the resolvent function. By using the error formula, we propose some greedy algorithms for the interpolatory H_∞ norm MOR.

READ FULL TEXT

page 1

page 2

page 3

page 4

04/06/2020

On an optimal interpolation formula in K_2(P_2) space

The paper is devoted to the construction of an optimal interpolation for...
08/21/2017

Economic Design of Memory-Type Control Charts: The Fallacy of the Formula Proposed by Lorenzen and Vance (1986)

The memory-type control charts, such as EWMA and CUSUM, are powerful too...
12/28/2021

A New First Order Taylor-like Theorem With An Optimized Reduced Remainder

This paper is devoted to a new first order Taylor-like formula where the...
11/04/2021

A Sound Up-to-n,δ Bisimilarity for PCTL

We tackle the problem of establishing the soundness of approximate bisim...
04/14/2002

Belief Revision and Rational Inference

The (extended) AGM postulates for belief revision seem to deal with the ...
02/01/2022

On a formula for moments of the multivariate normal distribution generalizing Stein's lemma and Isserlis theorem

We prove a formula for the evaluation of averages containing a scalar fu...
07/05/2022

Confluent Vandermonde with Arnoldi

In this note, we extend the Vandermonde with Arnoldi method recently adv...