The motivation for this work is the desire to e?ciently solve systems of nonlinear equations that have both linear and nonlinear variables. This type of system is sometimes referred to as a separable system of nonlinear equations. In this work, the Shen-Ypma algorithm is extended to overdetermined separable systems, establishing the connection with the Golub-Pereyra variable projection method. A new FORTRAN implementation of the method is provided and early developments in the field are surveyed.

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