Singular Value Decomposition (SVD) factorizes any real matrix A into a product of three matrices S, U and V. Matrix S is a diagonal matrix containing the singular values matrix A arranged in descending form. Matrices U and V are orthogonal such as U contains the left singular vectors whereas V contains the right singular vectors. This work uses One Sided Jacobi algorithm to calculate SVD. The Jacobi rotations are calculated on every 2 × 2 submatrix to zero out all non-zero off-diagonal elements of the original matrix. Number of iterations implemented are 5 which are used to converge. The high accuracy of the algorithm can be seen from the error plot.
- Floating Point function and MATLAB function: 10-16 – 10-15
- Floating Point function and Fixed Point function: 10-6 – 10-4
Implemented QR Decomposition using Householder Reflections algorithm and Givens Rotations algorithm
n=4
n=5
n=10
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