A new recursive eigendecomposition algorithm of Complex Hermitian Tœplitz matrices is studied. Based on Trench’s inversion of Tœplitz matrices from their autoregressive analysis, we have developed a fast recursive iterative algorithm that takes into account the rank-one modification of successive order Toeplitz matrices. To speed up the computational time and to increase numerical stability of ...

For a separated sequence Λ = {λk}k∈Z of real numbers there is a close link between the lower and upper densities D−(Λ), D(Λ) and the frame properties of the exponentials {ek}k∈Z: in fact, {ek}k∈Z is a frame for its closed linear span in L(−γ, γ) for any γ ∈]0, πD−(Λ)[∪]πD+(Λ),∞[. We consider a classical example presented already by Levinson [10] with D−(Λ) = D(Λ) = 1; in this case, the frame pr...

One gives a recursive algorithm for the computation of the first and second order derivatives of the entropy of a periodic autoregressive process with respect to the autocovariances. It is an extension of the periodic LevinsonDurbin algorithm. The algorithm has been developed for use at one of the steps of an entropy maximization method developed by the authors. Numerical examples of entropy ma...

Human daily social interaction is anchored in interpersonal discourse, and linguistic politeness thus vital to our everyday language including face-to-face computer-mediated communication. Politeness conventions emails are not being taught students seem be a work-in-progress. In power-asymmetrical context such as student-teacher interaction, requests pragmatically demanding, complex, inherently...

Language politeness is a critical element to be incorporated in communication for its worth across social status, power, or position. In this study, WhatsApp text conversations between students and lecturers were utilised analysing strategies used by the students. Purposive sampling which involved texts from two classes of English Oral Presentation (ELC590) subject was conducted messages thirty...