Three Hundred Years Later, a Tool from Isaac Newton Gets an Update
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Summary
A new algorithm built by US researchers could extend the capabilities of a centuries-old technique for finding minimum values in complex mathematical functions.
The work builds on Isaac Newton’s method for rapidly homing in on a curve’s lowest point by iteratively refining a Taylor series expansion of the function.
Rather than relying on derivatives, the team added a fudge factor to create a sum-of-squares function that is easier to work with and remains true to the original function.
By increasing this fudge factor, the team was able to work with arbitrarily many derivatives, while ensuring that the minimum could be found more quickly than with existing technologies.
While the research remains largely theoretical, the team believes it could become more practically applicable as computational methods improve over coming decades.
