P. M. Nguyen, T. T. Le, L. H. Nguyen, M. V. Klibanov
{"title":"Numerical Differentiation by the Polynomial-Exponential Basis","authors":"P. M. Nguyen, T. T. Le, L. H. Nguyen, M. V. Klibanov","doi":"10.1134/S1990478923040191","DOIUrl":null,"url":null,"abstract":"<p> Our objective is to calculate the derivatives of data corrupted by noise. This is\na challenging task as even small amounts of noise can result in significant errors in the\ncomputation. This is mainly due to the randomness of the noise, which can result in\nhigh-frequency fluctuations. To overcome this challenge, we suggest an approach that involves\napproximating the data by eliminating high-frequency terms from the Fourier expansion of the\ngiven data with respect to the polynomial-exponential basis. This truncation method helps to\nregularize the issue, while the use of the polynomial-exponential basis ensures accuracy in the\ncomputation. We demonstrate the effectiveness of our approach through numerical examples in\none and two dimensions.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"928 - 942"},"PeriodicalIF":0.5800,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923040191","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
Our objective is to calculate the derivatives of data corrupted by noise. This is
a challenging task as even small amounts of noise can result in significant errors in the
computation. This is mainly due to the randomness of the noise, which can result in
high-frequency fluctuations. To overcome this challenge, we suggest an approach that involves
approximating the data by eliminating high-frequency terms from the Fourier expansion of the
given data with respect to the polynomial-exponential basis. This truncation method helps to
regularize the issue, while the use of the polynomial-exponential basis ensures accuracy in the
computation. We demonstrate the effectiveness of our approach through numerical examples in
one and two dimensions.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
