QR Decomposition

Matrix Decomposition

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

The Singular Value Decomposition and the QR Decomposition in the Extended Max Algebra

In this paper we present an alternative proof for the existence theorem of the singular value decomposition in the extended max algebra and we propose some possible extensions of the max-algebraic singular value decomposition. We also prove the existence of a kind of QR decomposition in the extended max algebra.

Kernel-based Weighted Discriminant Analysis with QR Decomposition and Its Application to Face Recognition

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 ...

The Qr Decomposition and the Singularvalue Decomposition in the Symmetrizedmax - plus Algebrab

The Analysis and Comparison of Algorithm in QR Decomposition

QR decomposition of matrix is one of the important problems in the field of matrix theory. Besides, there are also so many extensive applications that using QR decomposition. Because of that, there are many researchers have been studying about algorithm for this decomposition. Two of those researchers are Feng Tianxiang and Liu Hongxia. In their paper, they proposed new algorithm to make QR dec...

Through-Wall Image Enhancement Using Fuzzy and QR Decomposition

QR decomposition and fuzzy logic based scheme is proposed for through-wall image enhancement. QR decomposition is less complex compared to singular value decomposition. Fuzzy inference engine assigns weights to different overlapping subspaces. Quantitative measures and visual inspection are used to analyze existing and proposed techniques.