The rational Krylov sequence (RKS) method is a generalization of Arnoldi's method. It constructs an orthogonal reduction of a matrix pencil into an upper Hessenberg pencil. The RKS method is useful when the matrix pencil may be eeciently factored. This article considers approximately solving the resulting linear systems with iterative methods. We show that a Cayley transformation leads to a mor...

This paper presents a new statistical approach to the blind estimation of linear multiple-input multiple-output (MIMO) channels with finite impulse response. A matrix pencil is constructed from a set of fourth-order cumulant matrices of the channel output signals. The MIMO channel impulse responses can then be efficiently estimated from the generalized eigendecomposition of this cumulant matrix...

As far as algorithmic thinking is bound by symbolic paper-and-pencil operations, the Church-Turing thesis appears to hold. But is physics, and even more so, is the human mind, bound by symbolic paper-and-pencil operations? What about the powers of the continuum, the quantum, and what about human intuition, human thought? These questions still remain unanswered. With the strong Artificial Intell...

We study wave propagation in periodic and frequency dependent materials. The approach in this paper leads to spectral analysis of a quadratic operator pencil where the spectral parameter relates to the quasimomentum and the frequency is a parameter. We show that the underlying operator has a discrete spectrum, where the eigenvalues are symmetrically placed with respect to the real and imaginary...

To assist students understand the difficult concepts of divided attention and interference, a new purpose built computer & mouse task is compared with an existing paper & pencil version, and yields complementary results. The pencil & paper task provides first-hand experience of divided attention and interference for the students. The computer & mouse task further extends the learning experience...

As far as algorithmic thinking is bound by symbolic paper-and-pencil operations, the Church-Turing thesis appears to hold. But is physics, and even more so, is the human mind, bound by symbolic paper-and-pencil operations? What about the powers of the continuum, the quantum, and what about human intuition, human thought? These questions still remain unanswered. With the strong Artificial Intell...

This paper presents an asymptotical analysis of the MUSIC and Pencil-MUSIC methods for estimating 2-D angles and polarizations using crossed dipoles. The explicit first order expressions for the variances of the MUSIC and Pencil-MUSIC estimates are derived. Both the theoretical and simulation results are used to analyze and compare the performances of the MUSIC and Pencil-MUSIC methods. A numbe...

In this paper, we give a numerically reliable algorithm to compute the zeros of a periodic descriptor system. The algorithm is a variant of the staircase algorithm applied to the system pencil of an equivalent lifted time-invariant state-space system and extracts a low-order pencil which contains the zeros (both 6nite and in6nite) as well as the Kronecker structure of the periodic descriptor sy...

The rational QZ method generalizes the by implicitly supporting subspace iteration. In this paper we extend introducing shifts and poles of higher multiplicity in Hessenberg pencil, which is a pencil consisting two matrices. result multishift, multipole iteration on block pencils allows one to stick real arithmetic for input pencil. combination with optimally packed aggressive early deflation a...

With smart devices being an essential part of our everyday lives, unsupervised access to the mobile sensors' data can result in a multitude side-channel attacks. In this paper, we study potential leaks from Apple Pencil (2nd generation) supported by iPad Pro, latest stylus pen which attaches body magnetically for charging. We observe that Pencil's affects magnetic readings sensed iPad's magneto...