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...

Recently, many studies are being conducted related to the method of inserting the digital watermark in the QR code. The QR code is made up of a simple repeating black and white module and has many differences compared to general images. In this paper, a watermarking algorithm that can increase the amount of information to be concealed by minimizing the degradation of QR code image quality is pr...

It has been shown in [4, 5, 6, 31] that the Hessenberg iterates of a companion matrix under the QR iterations have low off-diagonal rank structures. Such invariant rank structures were exploited therein to design fast QR iteration algorithms for finding eigenvalues of companion matrices. These algorithms require only O(n) storage and run in O(n) time where n is the dimension of the matrix. In t...

Quick response (QR) code is the prevalent trademark for a type of matrix barcode symbol. That code is always scanned to efficiently acquire data, especially for mobile device users. It involves the capabilities of data storage, reliable readability and strong error correction. This paper utilizes these properties of a QR code to propose an image tamper detection and recovery scheme for grayscal...

This paper is concerned with how the QR factors change when a real matrix A suffers from a left or right multiplicative perturbation, where A is assumed to have full column rank. It is proved that for a left multiplicative perturbation the relative changes in the QR factors in norm are no bigger than a small constant multiple of the norm of the difference between the perturbation and the identi...