The problem of computing the eigendecomposition of an N N symmetric matrix is cast as an unconstrained minimization of either of two performance measures. The K = N(N 1)=2 independent parameters represent angles of distinct Givens rotations. Gradient descent is applied to the minimization problem, step size bounds for local convergence are given, and similarities to LMS adaptive filtering are n...

We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DSTIV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from 2N log2 N +O(N...