Computing the Eigen Decomposition of a Symmetric Matrix in Fixed-point Arithmetic

Since a number of signal processing algorithms requiring the EVD of a symmetric matrix are implemented on fixedpoint DSPs, there is considerable interest in matrix diagonalization algorithms that can be implemented in fixed-point arithmetic. We propose modifications to the Jacobi Cyclic Row algorithm that favor a fixed-point implementation. We then compare the eigenvalues and eigenvectors obtained from the Jacobi Algorithm implemented in fixed-point arithmetic to ones obtained from a floating point algorithm. For the matrices considered, we find that the EVD obtained from the fixedpoint implementation matches closely a floating-point implementation of the EVD decomposition. We also give an estimate of computational complexity of the fixed point algorithm.