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Matrix chain multiplication is an optimization problem that can be solved using dynamic programming to determine the most efficient order for multiplying matrices. While the result of multiplying matrices is the same regardless of the parenthesized order, finding the optimal order can reduce the number of scalar multiplications needed. Associated matrix multiplication involves determining different parenthesized orders that result in the same overall multiplication, such as (A(BC)) and (AB(C)).
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- 5. MATRIX CHAIN MULTIPLICATION: Matrix chain multiplication is also called Matrix Chain Ordering Problem(MCOP). It is an optimization problem that can be solved using Dynamic programming. Here are many options because matrix multiplication is associated. In other words, no matter how the product is parenthesized, the result obtained will remain the same.
- 6. ASSOCIATED MULTIPLICATION: • Associated (A.B.C) A,B and C are number of multiplication. multiplication can be done as: A =5*4 B=4*6 C=6*2 Multiplication can be done as (A(BC)) = (AB(C)) (5*4(4*6.6*2)) = (5*4.4*6(6*2)) (20(24.12)) = (20.24(12)) (20(288)) = (480(12)) 5760 = 5760