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Better Algorithms through Faster Math

By Samuel Greengard
Communications of the ACM, June 2023, Vol. 66 No. 6, Pages 11-13
10.1145/3591213
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bursts of light from circuitry, illustration — Credit: Andrew Ostrovsky

Developing faster algorithms is an important but elusive goal for data scientists. The ability to accelerate complex computing tasks and reduce latency has far-reaching ramifications in areas such as natural language processing, video streaming, autonomous robotics, gaming, and extended reality.

Yet for all the hype surrounding computer algorithms and the increasingly sophisticated ways they operate, a basic fact stands out: these algorithms are typically built atop matrix multiplication, a basic type of linear algebra. The underlying mathematical framework has not changed a great deal since the inception of computing—and finding more efficient formulas has proved elusive.

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