Hanoch Lev-Ari

Fast Parallel Algorithms for QR and Triangular Factorization

We present a family of new fast algorithms for QR factorization of certain structured matrices, including rectangular Toeplitz matrices and a variety of other Toeplitz-like matrices. It possesses a very regular structure, and appears to be very convenient for parallel implementation. Moreover it is shown that the same architecture can be used for either triangular factorization or QR factorization. Our approach separates the conceptual and implementational aspects of the problem. Our analysis reveals a variety of algorithmic implementations of the basic procedure, all with potentially different numerical properties that need further examination.Our approach is based on the observations that the matrix

Extension of the signal subspace speech enhancement approach to colored noise

{\bf R}

Lattice filter parameterization and modeling of nonstationary processes

in

Triangular Factorization of Structured Hermitian Matrices

{\bf A} = {\bf {QR}}

Randomized modulation in power electronic converters

is the Cholesky factor of

Optimal tracking of time-varying channels: a frequency domain approach for known and new algorithms

{\bf A}^T {\bf A}

Traveling-Wave-Based Fault-Location Technique for Transmission Grids Via Wide-Area Synchronized Voltage Measurements

and that fast algorithms for Cholesky factorization of positive definite Toeplitz and certain “close-to-Toeplitz” matrices are readily obtained via a so-called displacement representation of matrices. In this paper we show that if

Hilbert space techniques for modeling and compensation of reactive power in energy processing systems

{\bf A}

Generalized Bezoutians and families of efficient zero-location procedures

is Toeplitz or is expressed in suitable displacement form then

Adaptive Laguerre-lattice filters

{\bf A}^T {\bf A}