Focuses on finding the minimum number of arithmetic operations needed to perform the computation and on finding a better algorithm when improvement is possible. The author concentrates on that class of problems concerned with computing a system of bilinear forms.Results that lead to applications in the area of signal processing are emphasized, since (1) even a modest reduction in the execution time of signal processing problems could have practical significance; (2) results in this area are relatively new and are scattered in journal articles; and (3) this emphasis indicates the flavor of complexity of computation.