Generalised norm resolvent convergence: comparison of different concepts
Olaf Post, Sebastian Zimmer
TL;DR
This paper proves the equivalence of two concepts of generalized norm resolvent convergence, analyzes their convergence speeds, and illustrates the results with numerous examples.
Contribution
It establishes the equivalence of two different concepts of generalized norm resolvent convergence and compares their convergence speeds.
Findings
The two concepts are equivalent.
Conditions for equal convergence speeds are provided.
Numerous examples illustrate the theoretical results.
Abstract
In this paper, we show that the two concepts of generalised norm resolvent convergence introduced by Weidmann and the first author of this paper are equivalent. We also focus on the convergence speed and provide conditions under which the convergence speed is the same for both concepts. We illustrate the abstract results by a large number of examples.
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Taxonomy
TopicsMatrix Theory and Algorithms · Stability and Control of Uncertain Systems · Numerical methods in inverse problems