On conditions for optimality in least pth approximation withp → ∞

This paper presents a theoretical discussion of the necessary and sufficient conditions for optimality in generalized nonlinear leastpth approximation problems forp . In the limit, the conditions for a minimax approximation are derived, as is to be expected. Numerical examples involving the modeling of a linear time-invariant fourth-order system by a second-order model and the design of quarter-wave transmission-line transformers illustrate the results.This work was supported by the National Research Council of Canada under Grant No. A7239 and by a Frederick Gardner Cottrell Grant from the Research Corporation. This paper was presented at the 9th Annual Allerton Conference on Circuit and System Theory, Urbana, Illinois, October 6–8, 1971. The authors thank Mrs. J. R. Popovi for helping to correct Example 4.1.