In the function InnerProduct_SortAlg, we used std::sort to arrange the summands in order. Can you explain why this helps? What should the sort order be? What is the time complexity of this solution?...

In the function InnerProduct_SortAlg, we used std::sort to arrange the summands in order. Can you explain why this helps? What should the sort order be? What is the time complexity of this solution? Rewrite the matrix multiplication procedure in Listing 3.23 using the Kahan algorithm for summation. The broad group of definite integrals (7.51) of integrable functions f can be approximated by the following summation: where a , , nd . (7.52) Assuming division of the integration interval into a number N of equal partitions, the previous summation can be further simplified as follows. The point ci can be chosen as the middle point between the points xi and xi+1, as follows: Insert Eqs. (7.53)–(7.54) into Eq. (7.52), and implement a method for numerically computing the definite integrals for any function. Represent functions programmatically, as discussed in Section 3.14.9.