We explore the possibility of improving the accuracy of approximations of elements of exponentials of differential operators, by using a rational function, instead of a polynomial function, as the interpolating function. Since a rational function behaves more like a decaying exponential function, it seems logical that the approximation should be more accurate. Through the use of high accuracy rational interpolants, we experiment with a numerical integration method to determine explicitly whether the error produced by a rational type approximation will indeed be less than that produced by a polynomial type approximation.
","abstract_html":"<p>We explore the possibility of improving the accuracy of approximations of elements of exponentials of differential operators, by using a rational function, instead of a polynomial function, as the interpolating function. Since a rational function behaves more like a decaying exponential function, it seems logical that the approximation should be more accurate. Through the use of high accuracy rational interpolants, we experiment with a numerical integration method to determine explicitly whether the error produced by a rational type approximation will indeed be less than that produced by a polynomial type approximation.</p>","abstract_has_math":false,"creators":["Lanterman, Daniel Elwood"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["James Lambers","Huiqing Zhu","Haiyan Tian"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-01T07:00:00Z","date_published":"2012-05-01T07:00:00Z","updated_at":"2026-07-24T05:44:58Z","subjects":["Mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/387","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["James Lambers","Huiqing Zhu","Haiyan Tian"]},{"key":"dc:creator","label":"Author","values":["Lanterman, Daniel Elwood"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-10-24T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Physical Sciences and Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/387"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We explore the possibility of improving the accuracy of approximations of elements of exponentials of differential operators, by using a rational function, instead of a polynomial function, as the interpolating function. Since a rational function behaves more like a decaying exponential function, it seems logical that the approximation should be more accurate. Through the use of high accuracy rational interpolants, we experiment with a numerical integration method to determine explicitly whether the error produced by a rational type approximation will indeed be less than that produced by a polynomial type approximation.
"]},{"key":"dc:title","label":"Title","values":["Approximation of Elements of Exponentials of Differential Operators With Rational Quadrature"]}]}],"canonical_facts":{"dc:contributor":["James Lambers","Huiqing Zhu","Haiyan Tian"],"dc:creator":["Lanterman, Daniel Elwood"],"dc:date.available":["2018-10-24T07:00:00Z"],"dc:description.abstract":["We explore the possibility of improving the accuracy of approximations of elements of exponentials of differential operators, by using a rational function, instead of a polynomial function, as the interpolating function. Since a rational function behaves more like a decaying exponential function, it seems logical that the approximation should be more accurate. Through the use of high accuracy rational interpolants, we experiment with a numerical integration method to determine explicitly whether the error produced by a rational type approximation will indeed be less than that produced by a polynomial type approximation.
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