Question

Q: "Discuss your background about "investigate the performance of several C implementations of matrix multiplication and compare them to the performance of matrix multiplication in Java"

I need to compare between Java and C program performing Matrix Multiplication.I need background about this topic. Not code! I need professional writing about this topic. thanks

Answer 1

Answer:-

Matrix multiplication in C language: C program to multiply two matrices (two-dimensional arrays) which will be entered by a user. The user will enter the order of a matrix and then its elements and similarly inputs the second matrix. If the orders of the matrices are such that they can't be multiplied by each other, then an error message is displayed. You may have studied the method to multiply matrices in Mathematics.

To multiply two matrices, the number of columns of first matrix should be equal to the number of rows to second matrix. This program displays the error until the number of columns of first matrix is equal to the number of rows of second matrix.

This C program performs matrix multiplication. In matrix multiplication, we take two matrices of order m*n and p*q respectively to find a resultant matrix of the order m*q where n is equal to p . Time Complexity of this algorithm is O(n³).

Java program to multiply two matrices: before multiplication matrices are checked whether they can be multiplied or not. We will use the simplest method of multiplication, there are more efficient algorithms available. Also this approach isn't recommended for sparse matrices which contains a large number of elements as zero.

Let the two matrix to be multiplied be A and B. Let A be a matrix of order d*e - d rows and e columns and B be the second matrix of order e*f. Note that the number of columns in the first matrix should be the same as the number of rows in the second matrix. The product matrix will be of order d*f. Now, our task is to find what numbers go into each of the positions of matrix C with d rows and f columns. We use an outer loop with loop counter i ranging from 0 to d. An inner loop has the loop counter j ranging from 0 to f. At any iteration of the loop, i refers to the row number and j to the column number of the position in matrix C that we are trying to fill. Now, within the body of the inner loop, we have to write some code which will calculate the value to be filled. This body will in turn consist of a loop. When we are obtaining the value at C[i][j], row i of matrix A and column j of matrix B are multiplied element wise.