In the rst part 13] of the paper transformationsmappingToeplitz and Toeplitz-plus-Hankel matrices into generalizedCauchy matrices were studied. In this second part fast algorithms for LU-factorization and inversion of generalized Cauchy matrices are discussed. It is shown that the combinationof transformation pivoting techniques leads to algorithms for indeenite Toeplitz and Toeplitz-plus-Hanke...

1970 Toeplitz-Plus-Hankel Matrix Recovery for Green’s Function Computations on General Substrates By R. Y. Zhang and J. K. White |INVITED PAPER| In this paper, the authors show that all elements of an implicitly defined Toeplitz-plus-Hankel (TPH) matrix can be recovered by sampling four or five carefully selected columns, and then using a linear least squares scheme to recover the rest of the m...

With the change of variables U = U*q, substitution into (21) results in UCU*q = Ud. Consequently, the solution vector U of (20) can be obtained from the solution vector q of (22) or q can be obtained from U. Note that if a system of real equations is Toeplitz-plus-Hankel (T + H) , where T i s symmetric Toeplitz and H i s skew-centrosym-metric Hankel, then the equations may be transformed into H...

In this paper, we consider some inverse singular value problems for Toeplitz-related matrices. We construct a Toeplitz-plus-Hankel matrix from prescribed singular values including a zero singular value. Then we find a solution to the inverse singular value problem for Toeplitz matrices which have double singular values including a double zero singular value.

An efficient method for the design of FIR filters satisfying prescribed magnitude and phase specifications is described. The method involves formulating an objective function in a quadratic form. The filter coefficients are obtained by solving a system of linear equations which involves either a Toeplitz matrix or a Toeplitz-plus-Hankel matrix. The computational complexity associated with such ...

Abstract It is well-known that the finite difference discretization of Laplacian eigenvalue problem ? ?u = ?u leads to a matrix (EVP) Ax ?x where A Toeplitz-plus-Hankel. Analytical solutions tridiagonal matrices with various boundary conditions are given in recent work Strang and MacNamara. We generalize results develop analytical certain generalized problems (GEVPs) ?Bx which arise from elemen...

When the heat equation and wave equation are approximated by ut = −Ku and utt = −Ku (discrete in space), the solution operators involve e−Kt, √K, cos(√Kt), and sinc( √ Kt). We compute these four matrices and find accurate approximations with a variety of boundary conditions. The second difference matrix K is Toeplitz (shift-invariant) for Dirichlet boundary conditions, but we show why e−Kt also...

We show that every n × n matrix is generically a product of n/2 + 1 Toeplitz matrices and always a product of at most 2n + 5 Toeplitz matrices. The same result holds true if the word ‘Toeplitz’ is replaced by ‘Hankel,’ and the generic bound n/2 + 1 is sharp. We will see that these decompositions into Toeplitz or Hankel factors are unusual: We may not, in general, replace the subspace of Toeplit...

Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical analytic arguments it is demonstrated that spectral statistics all these intermediate type, characterized by (i) level repulsion at small distances, (ii) an exponential decrease the nearest-neighbor distributions large...