smt: a Matlab structured matrices toolbox

We introduce the smt toolbox for Matlab. It implements optimized storage and fast arithmetics for circulant and Toeplitz matrices, and is intended to be transparent to the user and easily extensible. It also provides a set of test matrices, computation of circulant preconditioners, and two fast algorithms for Toeplitz linear systems.Comment: 19 pages, 1 figure, 1 typo corrected in the abstrac

Personalizing Cancer Pain Therapy: Insights from the Rational Use of Analgesics (RUA) Group

Introduction: A previous Delphi survey from the Rational Use of Analgesics (RUA) project involving Italian palliative care specialists revealed some discrepancies between current guidelines and clinical practice with a lack of consensus on items regarding the use of strong opioids in treating cancer pain. Those results represented the basis for a new Delphi study addressing a better approach to pain treatment in patients with cancer. Methods: The study consisted of a two-round multidisciplinary Delphi study. Specialists rated their agreement with a set of 17 statements using a 5-point Likert scale (0 = totally disagree and 4 = totally agree). Consensus on a statement was achieved if the median consensus score (MCS) (expressed as value at which at least 50% of participants agreed) was at least 4 and the interquartile range (IQR) was 3–4. Results: This survey included input from 186 palliative care specialists representing all Italian territory. Consensus was reached on seven statements. More than 70% of participants agreed with the use of low dose of strong opioids in moderate pain treatment and valued transdermal route as an effective option when the oral route is not available. There was strong consensus on the importance of knowing opioid pharmacokinetics for therapy personalization and on identifying immediate-release opioids as key for tailoring therapy to patients’ needs. Limited agreement was reached on items regarding breakthrough pain and the management of opioid-induced bowel dysfunction. Conclusion: These findings may assist clinicians in applying clinical evidence to routine care settings and call for a reappraisal of current pain treatment recommendations with the final aim of optimizing the clinical use of strong opioids in patients with cancer

On the kernel of vector epsilon-algorithm and related topics

The vector epsilon-algorithm of Wynn is a powerful method for accelerating the convergence of vector sequences. Its kernel is the set of sequences which are transformed into constant sequences whose terms are their limits or antilimits. In 1971, a sufficient condition characterizing sequences in this kernel was given by McLeod. In this paper, we prove that such a condition is not necessary. Moreover, using Clifford algebra, we give a formula for the vector \epsilon_2-transformation, which is formally the same as in the scalar case, up to operations in a Clifford algebra. Hence, Aitken's \Delta_2 process is extended in this way to vectors. Then, we derive the explicit algebraic and geometric expressions of sequences of the kernel of the \epsilon_2-transformation. We also formulate a conjecture concerning the explicit algebraic expression of kernel of the vector epsilon-algorithm

Zeros of quadratic quasi-orthogonal order 2 polynomials

Corollary 2 in [1] states that for $-rac{3}{2} < lambda < -rac{1}{2}, n in mathbb{N}$, the quasi-orthogonal order 2 Gegenbauer polynomial $C_n^{(lambda)}(x)$ has $n-2$ real, distinct zeros in $(-1,1),$ one zero larger than $1$ and one zero smaller than $-1.$ This is correct provided $n geq 3,$ $n in mathbb{N},$ but does not hold when $n=2$ for every $lambda$ in the range $-rac{3}{2} < lambda < -rac{1}{2}.$ An elementary calculation shows that the quasi-orthogonal order $2$ Gegenbauer polynomial $C_2^{(lambda)}(x)$ has $2$ real, distinct zeros with one zero larger than $1$ and one zero smaller than $-1$ when $-1 < lambda < -rac{1}{2}$ and two distinct pure imaginary zeros when $-rac{3}{2} < lambda < -1.$ A similar error occurs in the proof of Corollary 4(i) in [1] relating to the location of the zeros of the quadratic quasi-orthogonal order $2$ Jacobi polynomial $P_{2}^{(alpha,eta)}(x)$, $-2 < alpha, eta < -1.$ Each error arises from a different incorrect application of Theorem VII due to Shohat (cf. [8, p. 472]). We discuss the Hilbert-Klein formulas (cf. [9, p. 145]) and indicate the overlap between two different stages of the migration process of the zeros of $C_n^{(lambda)}(x)$ from the real axis to the imaginary axis (see [4] Section 3) that occurs when $n=2.

A program for solving the L2 reduced-order problem with fixed denominator degree

A set of necessary conditions that must be satisfied by the L2 optimal rational transfer matrix approximating a given higher-order transfer matrix, is briefly described. On its basis, an efficient iterative numerical algorithm has been obtained and implemented using standard MATLAB functions. The purpose of this contribution is to make the related computer program available and to illustrate some significant applications

Quasi-orthogonality with applications to some families of classical orthogonal polynomials

In this paper, we study the quasi-orthogonality of orthogonal polynomials. New results on the location of their zeros are given in two particular cases. Then these results are applied to Gegenbauer, Jacobi and Laguerre polynomials when the restrictions on the parameters involved in their definitions are not satisfied. The corresponding weight functions are investigated and the location of their zeros is discussed

Results of the application of an algorithm for L2 model reduction

An algorithm for L2-optimal model reduction in frequency domain is outlined. Some significant examples are illustrated to show the performance of the method and to compare the related results with those obtained using alternative techniques