[15] They benefit a very wide range of users through their incorporation into software including MATLAB, Maple, Wolfram Mathematica, GNU Octave, the R programming language, SciPy, and others.

[21] In 2013, he was the recipient of the ACM/IEEE Ken Kennedy Award for his leadership in designing and promoting standards for mathematical software used to solve numerical problems common to high-performance computing.

[19] Dongarra was elected a Fellow of the American Association for the Advancement of Science (AAAS), the Association for Computing Machinery (ACM), the Society for Industrial and Applied Mathematics (SIAM), and the Institute of Electrical and Electronics Engineers (IEEE) and a foreign member of the Russian Academy of Sciences and a foreign member of the Royal Society (ForMemRS).

[8] In 2001, he was elected a member of the US National Academy of Engineering for contributions to numerical software, parallel and distributed computation, and problem-solving environments.

[23] In 2023, Dongarra was elected to the U.S. National Academy of Sciences in recognition of his distinguished and continuing achievements in original research in the field of high-performance computing.

[25] Dongarra received the 2021 Turing Award "for pioneering contributions to numerical algorithms and libraries that enabled high performance computational software to keep pace with exponential hardware improvements for over four decades.".