Sliding window formulations of the fast QR and fast QR-lattice algorithms are presented. The derivations are based on the partial triangularization of raw data matrices. Three methods for window downdating are discussed: the method of plane hyperbolic rotations, the Chambers’ method, and the LINPACK algorithm. A numerically ill-conditioned stationary signal and a speech signal are used in finit...

We study the long time behavior of the Wasserstein gradient flow for an energy functional consisting of two components: particles are attracted to a fixed profile ω by means of an interaction kernel ψa(z) = |z|a , and they repel each other by means of another kernel ψr(z) = |z|r . We focus on the case of one space dimension and assume that 1 ≤ qr ≤ qa ≤ 2. Our main result is that the flow conve...

Virtual QR Code Stores are currently expanding globally and it is commonplace in the market to put emphasis on purely hedonic product assortments. This practice reflects the widespread assumption that hedonic products should be more effective to stimulate purchases because they facilitate impulse buying behavior. Contrary to this argumentation, the results of our study demonstrate that purchasi...

This paper presents a small-bulge multishift variation of the multishift QR algorithm that avoids the phenomenon of shift blurring, which retards convergence and limits the number of simultaneous shifts. It replaces the large diagonal bulge in the multishift QR sweep with a chain of many small bulges. The small-bulge multishift QR sweep admits nearly any number of simultaneous shifts—even hundr...

23.1 Let A be a nonsingular square matrix and let A = QR and A∗A = U∗U be QR and cholesky factorizations, respectively, with the usual normalization rjj, ujj > 0. Is it true or false that R = U? Solution: It is true. Since A is nonsingular, it will have a unique QR factorization with rjj > 0. Then we have A∗A = R∗Q∗QR = R∗R because Q is a unitary matrix. On the other hand, it is easy to see tha...

Fast QR decomposition algorithms based on backward prediction errors are well known for their good numerical behavior and low complexity. This paper examines two different versions of the fast QR algorithm based on a priori backward prediction errors as well as other two corresponding versions of the fast QR algorithm based on a posteriori backward prediction errors. The main matrix equations a...

Due to the greater in vitro activity of ciprofloxacin than that of levofloxacin against Pseudomonas aeruginosa, the likelihood of isolating a clinical strain of quinolone-resistant (QR) P. aeruginosa might be greater after exposure to levofloxacin than ciprofloxacin. We examined the risk of isolating QR P. aeruginosa in association with prior levofloxacin or ciprofloxacin exposure. A case-case-...

Kernel discriminant analysis (KDA) is a widely used approach in feature extraction problems. However, for high-dimensional multi-class tasks, such as faces recognition, traditional KDA algorithms have a limitation that the Fisher criterion is non-optimal with respect to classification rate. Moreover, they suffer from the small sample size problem. This paper presents two variants of KDA called ...

BACKGROUND Since their creation more than 20 years ago, the proliferation of Quick Response (QR) codes has expanded tremendously. Little was found in the literature to support the innovative use of QR coding in the classroom or in health care provision. Thus, the authors created a doctoral-level practicum experience using QR coding to create interactive, individualized patient or provider resou...