We present normwise and componentwise perturbation bounds for the hyperbolic QR factorization by using a new approach. The explicit expressions of mixed and componentwise condition numbers for the hyperbolic QR factorization are derived.

A = PUP∗, where P∗P = I and U is upper triangular, then the eigenvalues of A are given by the diagonal elements of U. The QR method developed by Francis in 1960’s [4] is classified as one of the topten developments in computation in the 20th century. The performance and robustness is still actively improved within the numerical linear algebra research community. We will now introduce the QR-met...

Natural isothiocyanates, produced during plant tissue damage from methionine-derived glucosinolates, are potent inducers of mammalian phase 2 detoxification enzymes such as quinone reductase (QR). A greatly simplified bioassay for glucosinolates based on induction and colorimetric detection of QR activity in murine hepatoma cells is described. It is demonstrated that excised leaf disks of Arabi...

BACKGROUND Quercetin (QR), is a polyphenolic flavonoid compound which is found in large amounts in certain foods, and protects against oxidative stress. The current study was conducted to determine whether Quercetin can possibly exert hepatoprotective and antioxidant activity against acrylamide (ACR) induced toxicity in rats. METHODS Four groups of Wistar rats consisting of six rats each: (i)...

Our previous study demonstrated that methanolic extract of Chrysanthemum zawadskii Herbich var. latilobum Kitamura (Compositae) has the potential to induce detoxifying enzymes such as NAD(P)H:(quinone acceptor) oxidoreductase 1 (EC 1.6.99.2) (NQO1, QR) and glutathione S-transferase (GST). In this study we further fractionated methanolic extract of Chrysanthemum zawadskii and investigated the de...

For an Hermitian matrix the QR transform is diagonally similar to two steps of the LR transforms. Even for non-Hermitian matrices the QR transform may be written in rational form.

We extend, in the context of a connected real semisimple Lie group, some results on the QR iteration and the Cholesky iteration of a nonsingular matrix. A group theoretic understanding of the abstract mechanisms of the iterations is obtained.