Explain the algorithm for matrix multiplication for parallel computational model. What is its complexity?

Matrix multiplication is a fundamental operation in computational science, widely used in various domains like scientific computing, engineering, graphics, and data analysis. Efficiently performing matrix multiplication is crucial, especially when dealing with large datasets. Parallel computing offers significant advantages by distributing the workload among multiple processors, thereby reducing computation time.

Basics of Matrix Multiplication

Given two matrices AA and BB:

• AA is of dimension m×nm \times n,
• BB is of dimension n×pn \times p,
• The product C=A×BC = A \times B will have dimensions m×pm \times p.

Each element C[i][j]C[i][j] in the resulting matrix CC is computed as:

C[i][j]=∑k=1nA[i][k]×B[k][j]C[i][j] = \sum_{k=1}^{n} A[i][k] \times B[k][j]

Sequential Algorithm Complexity

In the sequential model, computing each element of CC requires nn multiplications and additions. Since there are m×pm \times p elements in CC, the time complexity of the sequential _________ ________ ___ ____ ______.
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