Why do we use matrix chain multiplication?

The matrix chain multiplication problem generalizes to solving a more abstract problem: given a linear sequence of objects, an associative binary operation on those objects, and a way to compute the cost of performing that operation on any two given objects (as well as all partial results), compute the minimum cost way …

What are the various algorithms to solve matrix chain multiplication problems explain with example?

Example of Matrix Chain Multiplication

• Example: We are given the sequence {4, 10, 3, 12, 20, and 7}.
• Now product of 3 matrices:
• M [1, 3] =264.
• M [2, 4] = 1320.
• M [1, 4] =1080.
• Now Product of 5 matrices:
• Final Output is:
• Step 3: Computing Optimal Costs: let us assume that matrix Ai has dimension pi-1x pi for i=1, 2, 3….n.

What is the complexity of Strassen’s algorithm?

Hence, the complexity of Strassen’s matrix multiplication algorithm is O(nlog7).

What do you understand by Strassen matrix?

Strassen’s matrix is a Divide and Conquer method that helps us to multiply two matrices(of size n X n). You can refer to the link, for having the knowledge about Strassen’s Matrix first : Divide and Conquer | Set 5 (Strassen’s Matrix Multiplication)

Which of the following method can be used to solve the matrix chain multiplication problem?

Which of the following methods can be used to solve the matrix chain multiplication problem? Explanation: Dynamic Programming, Brute force, Recursion methods can be used to solve the matrix chain multiplication problem.

Which of the following matrix multiplication algorithm is faster Mcq?

What is the time complexity of the fastest known matrix multiplication algorithm? d) O(n!) Explanation: The Coppersmith-Winograd algorithm multiplies the matrices in O(n2.37) time. Several improvements have been made in the algorithm since 2010.

What is the recurrence relation used in Strassen’s algorithm?

Explanation: The recurrence relation used in Strassen’s algorithm is 7T(n/2) + Theta(n2) since there are only 7 recursive multiplications and Theta(n2) scalar additions and subtractions involved for computing the product.