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By choosing a specific structure for the approximant, we show that the resulting first-order optimality conditions can be interpreted as optimal\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varvec{\\mathcal {H}}_{\\varvec{2}}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msub>\n                            <mml:mrow>\n                              <mml:mi>H<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mrow>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    interpolation conditions for discrete-time dynamical systems. Connections to model reduction of discrete-time time-invariant delay systems are also established with particular emphasis on discretized linear systems obtained through the implicit Euler method, the midpoint method, and backward differentiation methods. A data-driven algorithm is developed to compute a (locally) optimal approximant. Our method is tested on three numerical experiments.\n                  <\/jats:p>","DOI":"10.1007\/s10444-025-10275-3","type":"journal-article","created":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T07:26:54Z","timestamp":1765265214000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Data-driven optimal approximation on Hardy spaces in simply connected domains"],"prefix":"10.1007","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5333-3074","authenticated-orcid":false,"given":"Alessandro","family":"Borghi","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9815-4897","authenticated-orcid":false,"given":"Tobias","family":"Breiten","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,12,9]]},"reference":[{"key":"10275_CR1","doi-asserted-by":"publisher","unstructured":"Antoulas, A.C., Beattie, C.A., Gugercin, S.: Interpolatory methods for model reduction. 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