Software Quality Metrics for Life-Cycle Cost-Reduction

This paper identifies factors or characteristics of which reliability is one, which comprise the quality of computer software. It then discusses their impact over the life of a software product, and describes a methodology for specifying them quantitatively, including them in system design, and measuring them during development. The methodology is still experimental, but is rapidly evolving toward application to all types of software. This paper emphasizes those factors of software quality which have greatest importance at the later stages of a software product's life.     

Scan-Along Polygonal Approximation for Data Compression of Electrocardiograms

Three fast and efficient "scan-along" algorithms for compressing digitized electrocardiographic data are described. These algorithms are "scan-along" in the sense that they produce the compressed data in real time as the electrocardiogram is generated. The algorithms are based on the minimum perimeter polygonal approximation for digitized curves. The approximation restricts the maximum error to be no greater than a specified value. Our algorithms achieve a compression ratio of ten on a database of 8000 5-beat abnormal electrocardiograms sampled at 250 Hz and a compression ratio of eleven on a database of 600 3-beat normal electrocardiograms (different from the preceding database) sampled at 500 Hz.     

Decision strategies that maximize the area under the LROC curve

For the 2-class detection problem (signal absent/present), the likelihood ratio is an ideal observer in that it minimizes Bayes risk for arbitrary costs and it maximizes the area under the receiver operating characteristic (ROC) curve [AUC]. The AUC-optimizing property makes it a valuable tool in imaging system optimization. If one considered a different task, namely, joint detection and localization of the signal, then it would be similarly valuable to have a decision strategy that optimized a relevant scalar figure of merit. We are interested in quantifying performance on decision tasks involving location uncertainty using the localization ROC (LROC) methodology. Therefore, we derive decision strategies that maximize the area under the LROC curve, A(LROC). We show that these decision strategies minimize Bayes risk under certain reasonable cost constraints. The detection-localization task is modeled as a decision problem in three increasingly realistic ways. In the first two models, we treat location as a discrete parameter having finitely many values resulting in an (L + 1) class classification problem. In our first simple model, we do not include search tolerance effects and in the second, more general, model, we do. In the third and most general model, we treat location as a continuous parameter and also include search tolerance effects. In all cases, the essential proof that the observer maximizes A(LROC) is obtained with a modified version of the Neyman-Pearson lemma. A separate form of proof is used to show that in all three cases, the decision strategy minimizes the Bayes risk under certain reasonable cost constraints.     

Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation

Summary. We study the role of preconditioning strategies recently developed for coercive problems in connection with a two-step iterative method, based on the Hermitian skew-Hermitian splitting (HSS) of the coefficient matrix, proposed by Bai, Golub and Ng for the solution of nonsymmetric linear systems whose real part is coercive. As a model problem we consider Finite Differences (FD) matrix sequences {A_n(a,p)}_n discretizing the elliptic (convection-diffusion) problem with being a plurirectangle of R^d with a(x) being a uniformly positive function and p(x) denoting the Reynolds function: here for plurirectangle we mean a connected union of rectangles in d dimensions with edges parallel to the axes. More precisely, in connection with preconditioned HSS/GMRES like methods, we consider the preconditioning sequence {P_n(a)}_n, P_n(a):= D_n^1/2(a)A_n(1,0) D_n^1/2(a) where D_n(a) is the suitably scaled main diagonal of A_n(a,0). If a(x) is positive and regular enough, then the preconditioned sequence shows a strong clustering at unity so that the sequence {P_n(a)}_n turns out to be a superlinear preconditioning sequence for {A_n(a,0)}_n where A_n(a,0) represents a good approximation of Re(A_n(a,p)) namely the real part of A_n(a,p). The computational interest is due to the fact that the preconditioned HSS method has a convergence behavior depending on the spectral properties of {P_n^-1(a)Re(A_n(a,p))}_n {P_n^-1(a)A_n(a,0)}_n: therefore the solution of a linear system with coefficient matrix A_n(a,p) is reduced to computations involving diagonals and to the use of fast Poisson solvers for {A_n(1,0)}_n.Some numerical experimentations confirm the optimality of the discussed proposal and its superiority with respect to existing techniques.Mathematics Subject Classification (1991): 65F10, 65N22, 15A18, 15A12, 47B65     

Stationary values of the ratio of quadratic forms subject to linear constraints

Sommario SiaA una matrice reale simmetrica di ordinen, B una matrice reale simmetrica di ordinen per cuix ^T B x>0 eC una matricen×p di rangor conrp. Si vogliono deteminare i vettorix per cui, JIMELè stazionaria eC ^T x= è il vettore nullo. È dato un algoritmo per generare un autosistema simmetrico i cui autovalori sono i valori stazionarì e per determinare i vettorix. Sono altresì presentate parecchie applicazioni dell'algoritmo.

---

---

Dedicated to Professor L. Collatz on his sixtieth birthday

---

This author was in part supported by the Atomic Energy Commission.