Multiplication Algorithm For Matrix

14 Jun, 2021

Do j i l -1 7. B2RnnandCABwherenis a power of two2We writeAandBas block matrices.

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Do m i i 0 4.

Multiplication algorithm for matrix. Strassens Matrix multiplication can be performed only on square matrices where n is a power of 2. Strassens had given another algorithm for finding the matrix multiplication. Example of Matrix multiplication.

The current best algorithmic bound isOn23728This algorithm however and other algorithms similar to ithave a verylarge multiplicative constant associated with the computation that it is notpractical to use. Let the input 4 matrices be A B C and D. Do for i 1 to n-l 1 6.

30000 There are 4 matrices of dimensions 10x20 20x30 30x40 and 40x30. Strassens Matrix Multiplication Algorithm The major work in matrix multiplication is multiplication only. Let us assume that somehow an e cient matrix multiplication kernel exists for matrices stored in Lh.

For k i to j-1 9. 3 Building-Blocks for Matrix Multiplication Consider the matrix multiplication C AB C where mh1 nh1 matrix C mh1 kh1 matrix A and kh1 nh1 matrix B are all stored in Lh1. So the idea is- if we reduced the number of multiplications then that will make the matrix multiplication faster.

The utility of Strassens formula is shown by its asymptotic superiority when order n of matrix reaches infinity. In this section we develop three distinct approaches for matrix multiplication kernels for matrices stored in Lh1. Idea - Block Matrix MultiplicationThe idea behind Strassens algorithm is in the formulationof matrix multiplication as a recursive problem.

Algorithm of Matrix Chain Multiplication MATRIX-CHAIN-ORDER p 1. Do q m i k m k 1 j p i-1 p k p j 10. This is nota tight upper bound on the algorithmic complexityof matrix multiplication.

MatrixMultiply A B. Order of both of the matrices are n n. Mij 8.

For l 2 to n l is the chain length 5. View each nnmatrix as a 22 matrix whose elements are n2 n2 matrices Apply the 22 algorithm recursively Tn 7Tn2 On2 Tn Onlg7On281. The minimum number of multiplications are obtained by putting parenthesis in following way A BCD -- 203010 402010 401030 Input.

For i 1 to n 3. Multiplication of matrices A and B C A B is such that each of its elements is denoted ij with 1 i m and 1 j n and is calculated follows. We rst cover a variant of the naive algorithmformulated in terms of block matrices and then parallelize it.

Column-sweep algorithm 3 Matrix-matrix multiplication Standard algorithm ijk-forms CPS343 Parallel and HPC Matrix Multiplication Spring 2020 332. Assume dimension of A is m x n dimension of B is p x q Begin if n is not same as p then exit otherwise define C matrix as m x q for i in range 0 to m - 1 do for j in range 0 to q 1 do for k in range 0 to p do C i j C i j A i k A k j done done done End. Divide X Y and Z into four n2 n2 matrices as represented below Z I J K L X A B C D and Y E F G H.

We say a matrix is m n if it has m rows and n columns. P 10 20 30 40 30 Output. For multiplying the two 22 dimension matrices Strassens used some formulas in which there are seven multiplication and eighteen addition subtraction and in brute force algorithm there is eight multiplication and four addition.

De nition of a matrix A matrix is a rectangular two-dimensional array of numbers.

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