Matrix Chain Multiplication Greedy Approach
You don't state why you think that your algorithm is correct. In fact, it is incorrect. Here is an example. Consider the problem of computing the product of matrices of dimensions $2\times 1$, $1\times 2$, $2 \times 5$. Your algorithm first multiplies the first two at a cost of $4$, and then multiplies the remaining matrices at a cost of $20$, to a total of $24$. In contrast, the other option has complexity $10 + 10 = 20$.

According to Wikipedia, Hu and Shing came up with an $O(n\log n)$ algorithm, which is more efficient than your algorithm, and moreover is provably correct.