Efficient Inversion of Matrix ϕ\phi-Functions of Low Order

The paper is concerned with efficient numerical methods for solving a linear system $\phi(A) x= b$, where $\phi(z)$ is a $\phi$-function and $A\in \mathbb R^{N\times N}$. In particular in this work we are interested in the computation of ${\phi(A)}^{-1} b$ for the case where $\phi(z)=\phi_1(z)=\displaystyle\frac{e^z-1}{z}, \quad \phi(z)=\phi_2(z)=\displaystyle\frac{e^z-1-z}{z^2}$. Under suitable conditions on the spectrum of $A$ we design fast algorithms for computing both ${\phi_\ell(A)}^{-1}$ and ${\phi_\ell(A)}^{-1} b$ based on Newton's iteration and Krylov-type methods, respectively. Adaptations of these schemes for structured matrices are considered. In particular the cases of banded and more generally quasiseparable matrices are investigated. Numerical results are presented to show the effectiveness of our proposed algorithms

A superfast solver for Sylvester's resultant linear systems generated by a stable and an anti-stable polynomial

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Exponential pseudo-splines: Looking beyond exponential B-splines

Pseudo-splines are a rich family of functions that allows the user to meet various demands for balancing polynomial reproduction (i.e., approximation power), regularity and support size. Such a family includes, as special members, B-spline functions, universally known for their usefulness in different fields of application. When replacing polynomial reproduction by exponential polynomial reproduction, a new family of functions is obtained. This new family is here constructed and called the family of exponential pseudo-splines. It is the nonstationary counterpart of (polynomial) pseudo-splines and includes exponential B-splines as a special subclass. In this work we provide a computational strategy for deriving the explicit expression of the Laurent polynomial sequence that identifies the family of exponential pseudo-spline nonstationary subdivision schemes. For this family we study its symmetry properties and perform its convergence and regularity analysis. Finally, we also show that the family of primal exponential pseudo-splines fills in the gap between exponential B-splines and interpolatory cardinal functions. This extends the analogous property of primal pseudo-spline stationary subdivision schemes

Deriving the respiratory sinus arrhythmia from the heartbeat time series using Empirical Mode Decomposition

Heart rate variability (HRV) is a well-known phenomenon whose characteristics are of great clinical relevance in pathophysiologic investigations. In particular, respiration is a powerful modulator of HRV contributing to the oscillations at highest frequency. Like almost all natural phenomena, HRV is the result of many nonlinearly interacting processes; therefore any linear analysis has the potential risk of underestimating, or even missing, a great amount of information content. Recently the technique of Empirical Mode Decomposition (EMD) has been proposed as a new tool for the analysis of nonlinear and nonstationary data. We applied EMD analysis to decompose the heartbeat intervals series, derived from one electrocardiographic (ECG) signal of 13 subjects, into their components in order to identify the modes associated with breathing. After each decomposition the mode showing the highest frequency and the corresponding respiratory signal were Hilbert transformed and the instantaneous phases extracted were then compared. The results obtained indicate a synchronization of order 1:1 between the two series proving the existence of phase and frequency coupling between the component associated with breathing and the respiratory signal itself in all subjects.Comment: 12 pages, 6 figures. Will be published on "Chaos, Solitons and Fractals

Significance of REM Sleep in Depression: Effects on Neurogenesis

No abstract availabl

Experimental Study of a Parallel Iterative Solver for Markov Chain Modeling

This paper presents the results of a preliminary experimental investigation of the performance of a stationary iterative method based on a block staircase splitting for solving singular systems of linear equations arising in Markov chain modelling. From the experiments presented, we can deduce that the method is well suited for solving block banded or more generally localized systems in a parallel computing environment. The parallel implementation has been benchmarked using several Markovian models

A QR based approach for the nonlinear eigenvalue problem

We describe a fast and numerically robust approach based on the structured QR eigenvalue algorithm for computing approximations of the eigenvalues of a holomorphic matrix-valued function inside the unit circle. Numerical experiments confirm the effectiveness of the proposed method