Functional equations in the theory of dynamic programming--XII: complex operators and min-max variation.

by Richard Ernest Bellman, Ronald F. Lehman


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An application of the functional-equation approach of dynamic programming to the study of variational problems associated with the Sturm-Liouville equation of second order with real coefficients. By obtaining the dependence of the Green's function on the interval length, the authors determine the corresponding dependence of the characteristic values and the characteristic functions, and similar results for vector-matrix systems. Min-max variation is used to apply the same general techniques to the study of equations with complex coefficients. It is shown that this method can be applied rigorously.

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