4,330 research outputs found
Inversion of Parahermitian matrices
Parahermitian matrices arise in broadband multiple-input multiple-output (MIMO) systems or array processing, and require inversion in some instances. In this paper, we apply a polynomial eigenvalue decomposition obtained by the sequential best rotation algorithm to decompose a parahermitian matrix into a product of two paraunitary, i.e.lossless and easily invertible matrices, and a diagonal polynomial matrix. The inversion of the overall parahermitian matrix therefore reduces to the inversion of auto-correlation sequences in this diagonal matrix. We investigate a number of different approaches to obtain this inversion, and and assessment of the numerical stability and complexity of the inversion process
Operator algebras and conjugacy problem for the pseudo-Anosov automorphisms of a surface
The conjugacy problem for the pseudo-Anosov automorphisms of a compact
surface is studied. To each pseudo-Anosov automorphism f, we assign an
AF-algebra A(f) (an operator algebra). It is proved that the assignment is
functorial, i.e. every f', conjugate to f, maps to an AF-algebra A(f'), which
is stably isomorphic to A(f). The new invariants of the conjugacy of the
pseudo-Anosov automorphisms are obtained from the known invariants of the
stable isomorphisms of the AF-algebras. Namely, the main invariant is a triple
(L, [I], K), where L is an order in the ring of integers in a real algebraic
number field K and [I] an equivalence class of the ideals in L. The numerical
invariants include the determinant D and the signature S, which we compute for
the case of the Anosov automorphisms. A question concerning the p-adic
invariants of the pseudo-Anosov automorphism is formulated.Comment: 23 pages, 1 fig;; to appear Pacific J. Math. arXiv admin note: text
overlap with arXiv:math/011022
Initial results on an MMSE precoding and equalisation approach to MIMO PLC channels
This paper addresses some initial experiments using polynomial matrix decompositions to construct MMSE precoders and equalisers for MIMO power line communications (PLC) channels. The proposed scheme is based on a Wiener formulation based on polynomial matrices, and recent results to design and implement such systems with polynomial matrix tools. Applied to the MIMO PLC channel, the strong spectral dynamics of the PLC system together with the long impulse responses contained in the MIMO system result in problems, such that diagonlisation and spectral majorisation is mostly achieved in bands of high energy, while low-energy bands can resist any diagonalisation efforts. We introduce the subband approach in order to deal with this problem. A representative example using a simulated MIMO PLC channel is presented
Tensor and Matrix Inversions with Applications
Higher order tensor inversion is possible for even order. We have shown that
a tensor group endowed with the Einstein (contracted) product is isomorphic to
the general linear group of degree . With the isomorphic group structures,
we derived new tensor decompositions which we have shown to be related to the
well-known canonical polyadic decomposition and multilinear SVD. Moreover,
within this group structure framework, multilinear systems are derived,
specifically, for solving high dimensional PDEs and large discrete quantum
models. We also address multilinear systems which do not fit the framework in
the least-squares sense, that is, when the tensor has an odd number of modes or
when the tensor has distinct dimensions in each modes. With the notion of
tensor inversion, multilinear systems are solvable. Numerically we solve
multilinear systems using iterative techniques, namely biconjugate gradient and
Jacobi methods in tensor format
- …