5 QR Decomposition 7 5.1 Householder Reflections and Givens Rotations . . . . . . . . . . . . . . . . . . . . . . . 8 5.2 Gram-Schmidt orthonormalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.3 QR Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.4 Least Square Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

This study focuses on the performance of two classical dense linear algebra algorithms, the LU and the QR factorizations, on multilevel hierarchical platforms. We first introduce a new model called Hierarchical Cluster Platform (HCP), encapsulating the characteristics of such platforms. The focus is set on reducing the communication requirements of studied algorithms at each level of the hierar...

Abstract The periodic QR algorithm is a strongly backward stable method for computing the eigenvalues of products of matrices, or equivalently for computing the eigenvalues of block cyclic matrices. The main purpose of this paper is to show that this algorithm is numerically equivalent to the standard QR algorithm. It will be demonstrated how this connection may be used to develop a better unde...

The present study aims to examine the influence of Quercetin (QR) in testis of Streptozotocin (STZ)induced diabetic rats. Diabetes was induced by a single injection of STZ (65 mg/kg, ip). Quercetin (25 and 50 mg/kg/day) was treated to normal and diabetic rats for 5 weeks. In serum, glucose, testosterone, Interleukin-6 (IL-6), Interleukin-1beta (IL-1β) and Tumor Necrosis Factor-α (TNF-α) levels ...

Human prostate cancer is characterized by an early and near-universal loss of expression of the phase 2 enzyme glutathione S-transferase-pi (GSTP1). We hypothesize that a mechanism-based prostate cancer preventive strategy could involve induction of phase 2 enzymes within the prostate to compensate for the loss of GSTP1 expression. NAD[P]H:(quinone-acceptor) oxidoreductase (quinone reductase or...

This study discusses a simple solution for the problem of shortage in learning resources for kindergarten teachers. Occasionally, kindergarten teachers cannot access proper resources by usual search methods as libraries or search engines. Furthermore, these methods require a long time and efforts for preparing. The study is expected to facilitate accessing learning resources. Moreover, it sugge...

While QR codes have recently become popular as a method of rapidly bringing information to consumer, they have the drawback that they contain no human readable content. This project concerns combining image data with QR codes while maintaining the machine readability of the code. We break each module down into pixels and halftone it to correspond to the image data while preserving the overall s...

The QR-algorithm is a renowned method for computing all eigenvalues of an arbitrary matrix. A preliminary unitary similarity transformation to Hessenberg form is indispensable for keeping the computational complexity of the subsequent QR-steps under control. In this paper, a whole new family of matrices, sharing the major qualities of Hessenberg matrices, will be put forward. This gives rise to...