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

Most commonly used face recognition algorithms are based on extraction of global features using eigenvalue decomposition of some relational matrix of image intensity values. Real time face recognition applications require a computationally efficient algorithm for eigenvalues generation. Fast principal component analysis (FPCA) is an algorithm for efficient generation of eigenvalues which improv...

Abstract : In this paper we present a combined feature extraction approach for an electronic tongue. The use of wavelet decomposition technique for feature extraction, followed by orthonormalization, decreases the number of classifier inputs to the multiplication of number of classes and number of sensors. This approach leads to a higher computational efficiency. Two experiments are presented t...

We present an e cient method for estimating nonlinearly entered parameters of a linear signal model corrupted by additive noise. The method uses the Gram-Schmidt orthonormalization procedure in combination with a number of iterations to de-bias and re-balance the coupling between non-orthogonal signal components e ciently. Projection interpretation is provided as rationale of the proposed itera...

An error analysis result is given for classical Gram–Schmidt factorization of a full rank matrix A into A = QR where Q is left orthogonal (has orthonormal columns) and R is upper triangular. The work presented here shows that the computed R satisfies RT R = AT A + E where E is an appropriately small backward error, but only if the diagonals of R are computed in a manner similar to Cholesky fact...

The parallel strong-scaling of iterative methods is often determined by the number global reductions at each iteration. Low-synch Gram–Schmidt algorithms are applied here to Arnoldi algorithm reduce and therefore improve solvers for nonsymmetric matrices such as GMRES Krylov–Schur methods. In context, QR factorization “left-looking” processes one column a time. Among generating an orthogonal ba...