MATHEMATICAL TRIPOS : PART II Michaelmas Term 2013 OPTIMIZATION AND CONTROL
نویسنده
چکیده
1. Suppose that the matrix Mk is of dimension nk × nk+1, k ∈ {1, . . . , h}. We wish to compute the product M1M2 · · ·Mh. Notice that the order of multiplication makes a difference. For example, if (n1, n2, n3, n4) = (1, 10, 1, 10), the calculation (M1M2)M3 requires 20 scalar multiplications, but the calculation M1(M2M3) requires 200 scalar multiplications. Indeed, multiplying a m × n matrix by a n × k matrix requires mnk scalar multiplications. Let F (n1, n2, . . . , nh+1; h) be the minimal total number of scalar multiplications required to compute M1M2 · · ·Mh. Explain why the dynamic programming equation is
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