An algorithm to compute the polar decomposition of a 3 × 3 matrix

We propose an algorithm for computing the polar decomposition of a 3 × 3 real matrix that is based on the connection between orthogonal matrices and quaternions. An important application is to 3D transformations in the level 3 Cascading Style Sheets specification used in web browsers. Our algorithm is numerically reliable and requires fewer arithmetic operations than the alternative of computing the polar decomposition via the singular value decomposition

Application of Gauss-Seidel method and singular value decomposition techniques to recursive least squares algorithm

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 1991.Thesis (Master's) -- Bilkent University, 1991.Includes bibliographical references leaves 42-43System identification algorithms are utilized in many practical and theoretical applications such as parameter estimation of sj'stems, adaptive control and signal processing . Least squares algorithm is one of the most popular algorithms in system identification, but it has some drawbacks such as large time consumption and small convergence rates. In this thesis, Gauss-Seidel method is implemented on recursive least squares algorithm and convergence behaviors of the resultant algorithms are analyzed. .Also in standard recursive least squares algorithm the excitation of modes are monitored using data matrices and this algorithm is accordingly altered. A parallel scheme is proposed in this analysis for efficient computation of the modes. The simulation results are also presented.Malaş, AtillaM.S