ОПТИМАЛЬНI МЕТОДИ ВIДНОВЛЕННЯ МIШАНИХ ПОХIДНИХ НЕПЕРIОДИЧНИХ ФУНКЦIЙ
DOI:
https://doi.org/10.17721/2706-9699.2022.2.16Ключові слова:
чисельне диференцiювання, полiном Лежандра, спектральна зрiзка, мiнiмальний радiус гальоркiнської iнформацiїАнотація
Дослiджується задача чисельного диференцiювання неперiодичних функцiй двох змiнних. Для вiдновлення мiшаних похiдних таких функцiй пропонується пiдхiд, що базується на iдеї спектральної зрiзки. В межах цього пiдходу будуєьться полiном Лежандра, ступiнь якого обирається так, щоб мiнiмiзувати похибку наближення. Встановлено, що побудованi в такий спосiб алгоритми чисельного диференцiювання є оптимальними як у сенсi точностi, так i обсягу задiяної гальоркiнської iнформацiї.
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