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Parallel Comput."],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>\n            This article is devoted to an approach to solving a problem of the efficiency of parallel computing. The theoretical basis of this approach is the concept of a\n            <jats:italic>Q<\/jats:italic>\n            -determinant. Any numerical algorithm has a\n            <jats:italic>Q<\/jats:italic>\n            -determinant. The\n            <jats:italic>Q<\/jats:italic>\n            -determinant of the algorithm has clear structure and is convenient for implementation. The\n            <jats:italic>Q<\/jats:italic>\n            -determinant consists of\n            <jats:italic>Q<\/jats:italic>\n            -terms. Their number is equal to the number of output data items. Each\n            <jats:italic>Q<\/jats:italic>\n            -term describes all possible ways to compute one of the output data items based on the input data.\n          <\/jats:p>\n          <jats:p>\n            We also describe a software\n            <jats:italic>Q<\/jats:italic>\n            -system for studying the parallelism resources of numerical algorithms. This system enables to compute and compare the parallelism resources of numerical algorithms. The application of the\n            <jats:italic>Q<\/jats:italic>\n            -system is shown on the example of numerical algorithms with different structures of\n            <jats:italic>Q<\/jats:italic>\n            -determinants. Furthermore, we suggest a method for designing of parallel programs for numerical algorithms. This method is based on a representation of a numerical algorithm in the form of a\n            <jats:italic>Q<\/jats:italic>\n            -determinant. As a result, we can obtain the program using the parallelism resource of the algorithm completely. Such programs are called\n            <jats:italic>Q<\/jats:italic>\n            -\n            <jats:italic>effective<\/jats:italic>\n            .\n          <\/jats:p>\n          <jats:p>The results of this research can be applied to increase the implementation efficiency of numerical algorithms, methods, as well as algorithmic problems on parallel computing systems.<\/jats:p>","DOI":"10.1145\/3583755","type":"journal-article","created":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T23:14:24Z","timestamp":1676502864000},"page":"1-64","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Investigation and Implementation of Parallelism Resources of Numerical Algorithms"],"prefix":"10.1145","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4717-0045","authenticated-orcid":false,"given":"Valentina","family":"Aleeva","sequence":"first","affiliation":[{"name":"South Ural State University (National Research University)"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2141-0132","authenticated-orcid":false,"given":"Rifkhat","family":"Aleev","sequence":"additional","affiliation":[{"name":"South Ural State University (National Research University)"}]}],"member":"320","published-online":{"date-parts":[[2023,6,20]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-25636-4_1"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-05807-4_48"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-36592-9_52"},{"key":"e_1_3_2_5_2","volume-title":"Analysis of Parallel Numerical Algorithms","author":"Aleeva Valentina N.","year":"1985","unstructured":"Valentina N. 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Q-Effective Implementation of the Jacobi Method for Solving SLAE on the Supercomputer \u201cTornado SUSU\u201d [in Russian].Master\u2019s thesis. School of Electronic Engineering and Computer Science. http:\/\/omega.sp.susu.ru\/publications\/bachelorthesis\/17-Lapteva.pdf."},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-99673-8_2"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-007-0271-4"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1109\/DCABES.2014.10"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.14529\/jsfi180204"},{"key":"e_1_3_2_21_2","unstructured":"William F. McColl. 1993. General purpose parallel computing. In Lectures on Parallel Computation Alan. M. Gibbons and Paul Spirakis (Eds). Cambridge International Series on Parallel Computation. 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