# New least-square algorithms

DOI: 10.1007/BF00935703

- Cite this article as:
- Davidon, W.C. J Optim Theory Appl (1976) 18: 187. doi:10.1007/BF00935703

## Abstract

New algorithms are presented for approximating the minimum of the sum of squares of*M* real and differentiable functions over an*N*-dimensional space. These algorithms update estimates for the location of a minimum after each one of the functions and its first derivatives are evaluated, in contrast with other least-square algorithms which evaluate all*M* functions and their derivatives at one point before using any of this information to make an update. These new algorithms give estimates which fluctuate about a minimum rather than converging to it. For many least-square problems, they give an adequate approximation for the solution more quickly than do other algorithms.