Ela How to Establish Universal Block - Matrix Factorizations ∗
نویسندگان
چکیده
A general method is presented for establishing universal factorization equalities for 2×2 and 4×4 block matrices. As applications, some universal factorization equalities for matrices over four-dimensional algebras are established, in particular, over the Hamiltonian quaternion algebra.
منابع مشابه
How to establish universal block-matrix factorizations
A general method is presented for establishing universal factorization equalities for 2×2 and 4×4 block matrices. As applications, some universal factorization equalities for matrices over four-dimensional algebras are established, in particular, over the Hamiltonian quaternion algebra.
متن کاملWZ factorization via Abay-Broyden-Spedicato algorithms
Classes of Abaffy-Broyden-Spedicato (ABS) methods have been introduced for solving linear systems of equations. The algorithms are powerful methods for developing matrix factorizations and many fundamental numerical linear algebra processes. Here, we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW factorizations of a nonsingular matrix as well as...
متن کاملEla a Newton Method for Canonical Wiener-hopf and Spectral Factorization of Matrix Polynomials
The paper presents a novel Newton method for constructing canonical Wiener-Hopf factorizations of complex matrix polynomials and spectral factorizations of positive definite matrix polynomials. The factorizations are the ones needed for discrete-time linear systems and hence with respect to the unit circle. The Jacobi matrix is analyzed, and the convergence of the method is proved and tested nu...
متن کاملBlock LU factorizations of M-matrices
It is well known that any nonsingular M–matrix admits an LU factorization into M–matrices (with L and U lower and upper triangular respectively) and any singular M–matrix is permutation similar to an M–matrix which admits an LU factorization into M–matrices. Varga and Cai establish necessary and sufficient conditions for a singular M–matrix (without permutation) to allow an LU factorization wit...
متن کاملIncomplete block factorization preconditioning for linear systems arising in the numerical solution of the Helmholtz equation
The application of the finite difference method to discretize the complex Helmholtz equation on a bounded region in the plane produces a linear system whose coefficient matrix is block tridiagonal and is some (complex) perturbation of an M-matrix. The matrix is also complex symmetric, and its real part is frequently indefinite. Conjugate gradient type methods are available for this kind of line...
متن کامل