We investigate the factored ADI iteration for large and sparse Sylvester equations. A novel low-rank expression for the associated Sylvester residual is established which enables cheap computations of the residual norm along the iteration, and which yields a reformulated factored ADI iteration. The application to generalized Sylvester equations is considered as well. We also discuss the efficie...

We derive a conjugate-gradient type algorithm to produce approximate least-squares (LS) solutions for an inconsistent generalized Sylvester-transpose matrix equation. The is always applicable any given initial and will arrive at LS solution within finite steps. When the equation has many solutions, can search one with minimal Frobenius-norm. Moreover, Y, find unique closest Y. Numerical experim...

Acknowledgements: During the research that led to the this paper, the first author was initially supported by the European Regional Development Fund through the programme  and by the PortugueseGovernment through the  (Fundação para a Ciência e a Tecnologia) under the project -/// and through an  Ciência  fellowship, and later supported by an  Investigador a...

Abstract We show that the discrete operator stemming from time-space discretization of evolutionary partial differential equations can be represented in terms a single Sylvester matrix equation. A novel solution strategy combines projection techniques with full exploitation entry-wise structure involved coefficient matrices is proposed. The resulting scheme able to efficiently solve problems tr...

In this paper, the eigenvalues of row-inverted 2 × 2 Sylvester Hadamard matrices are derived. Especially when the sign of a single row or two rows of a 2×2 Sylvester Hadamard matrix are inverted, its eigenvalues are completely evaluated. As an example, we completely list all the eigenvalues of 256 different row-inverted Sylvester Hadamard matrices of size 8. Mathematics Subject Classification (...

Variational inference relies on flexible approximate posterior distributions. Normalizing flows provide a general recipe to construct flexible variational posteriors. We introduce Sylvester normalizing flows, which can be seen as a generalization of planar flows. Sylvester normalizing flows remove the well-known single-unit bottleneck from planar flows, making a single transformation much more ...

This paper presents equivalent forms of the Sylvester matrix equations. These equivalent forms allow us to use block linear methods for solving large Sylvester matrix equations. In each step of theses iterative methods we use global FOM or global GMRES algorithm for solving an auxiliary block matrix equations. Also, some numerical experiments for obtaining the numerical approximated solution of...

‎the global fom and gmres algorithms are among the effective‎ ‎methods to solve sylvester matrix equations‎. ‎in this paper‎, ‎we‎ ‎study these algorithms in the case that the coefficient matrices‎ ‎are real symmetric (real symmetric positive definite) and extract‎ ‎two cg-type algorithms for solving generalized sylvester matrix‎ ‎equations‎. ‎the proposed methods are iterative projection metho...

4 History of the Sylvester-Gallai Problem 6 4.1 Melchior’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4.2 Motzkin’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.3 Kelly and Moser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.4 Green and Tao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.5 How to describe 3-color ...