Square matrix

About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.

A Higher Order Iterative Method for Computing the Drazin Inverse

Abstract: A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper.

Noisy matrix completion using alternating minimization

Abstract: The task of matrix completion involves estimating the entries of a matrix, M ∈ ℝm×n, when a subset, Ω ⊂{(i,j):1≤i≤m,1≤j≤n} of the entries are observed. A particular set of low rank models for this task approximate the matrix as a product of two low rank matrices, M = UVT, where U ∈ ℝm×k and V ∈ ℝn×k and k ≪ min {m,n}. A popular algorithm of choice in practice for recovering M from the partially observed matrix using the low rank assumption is alternating least square (ALS) minimization, which involves optimizing over U and V in an alternating manner to minimize the squared error over observed entries while keeping the other factor fixed. Despite being widely experimented in practice, only recently were theoretical guarantees established bounding the error of the matrix estimated from ALS to that of the original matrix M. In this work we extend the results for a noiseless setting and provide the first guarantees for recovery under noise for alternating minimization. We specifically show that for well conditioned matrices corrupted by random noise of bounded Frobenius norm, if the number of observed entries is O(k7n log n), then the ALS algorithm recovers the original matrix within an error bound that depends on the norm of the noise matrix. The sample complexity is the same as derived in [7] for the noise-free matrix completion using ALS.

Method and apparatus for singular value decomposition of a channel matrix

Abstract: A method and apparatus for decomposing a channel matrix in a wireless communication system are disclosed. A channel matrix H is generated for channels between transmit antennas and receive antennas (202). A Heπnitian matrix A=HHH or A=HHn is created (204). A Jacobi process is cyclically performed on the matrix A to obtain Q and DA matrixes such that A=QDAQH (206). DA is a diagonal matrix obtained by singular value decomposition (SVD) on the A matrix. In each Jacobi transformation, real part diagonalization is performed to annihilate real parts of off-diagonal elements of the matrix and imaginary part diagonalization is performed to annihilate imaginary parts of off -diagonal elements of the matrix after the real part diagonalization. U, V and DH matrixes of H matrix are then calculated from the Q and DA matrices. DH is a diagonal matrix comprising singular values of the H matrix (208).

Efficient Solution of Linear Matrix Equations with Application to Multistatic Antenna Array Processing

Abstract: We present a computationally-efficient matrix-vector expression for the solution of a matrix linear least squares problem that arises in multistatic antenna array processing. Our derivation relies on an explicit new relation between Kronecker, Khatri-Rao and Schur-Hadamard matrix products, which involves a selection matrix (i.e., a subset of the columns of a permutation matrix). Moreover, we show that the same selection matrix also relates the vectorization-by-columns operator to the diagonal extraction operator, which plays a central role in our computationally- efficient solution.