{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:36:18Z","timestamp":1776728178654,"version":"3.51.2"},"reference-count":29,"publisher":"American Mathematical Society (AMS)","issue":"235","license":[{"start":{"date-parts":[[2002,3,9]],"date-time":"2002-03-09T00:00:00Z","timestamp":1015632000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    A new approach to the construction of finite-difference methods is presented. It is shown how the multi-point differentiators can generate regularizing algorithms with a stepsize\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h\">\n                        <mml:semantics>\n                          <mml:mi>h<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">h<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    being a regularization parameter. The explicitly computable estimation constants are given. Also an iteratively regularized scheme for solving the numerical differentiation problem in the form of Volterra integral equation is developed.\n                  <\/p>","DOI":"10.1090\/s0025-5718-01-01307-2","type":"journal-article","created":{"date-parts":[[2002,11,6]],"date-time":"2002-11-06T14:02:22Z","timestamp":1036591342000},"page":"1131-1153","source":"Crossref","is-referenced-by-count":122,"title":["On stable numerical differentiation"],"prefix":"10.1090","volume":"70","author":[{"given":"Alexander","family":"Ramm","sequence":"first","affiliation":[]},{"given":"Alexandra","family":"Smirnova","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,3,9]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"R. G. Airapetyan, A. G. Ramm, A. B. Smirnova, \u201cContinuous methods for solving nonlinear ill-posed problems\u201d, Operator theory and applications, Fields Institute Communications, 25, Amer. Math. 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