This dissertation focuses on a widely used linear algebra kernel to solve linear systems, that is the LU decomposition. Usually, to perform such a computation one uses the Gaussian elimination with partial pivoting (GEPP). The backward stability of GEPP depends on a quantity which is referred to as the growth factor, it is known that in general GEPP leads to modest element growth in practice. H...

We perform a theoretical investigation on the Goos-Häenchen shift (the lateral shift) in one-dimensional photonic crystals (1DPCs) containing left-handed (LH) metamaterials. The effect was studied by use of a Gaussian beam. We show that the giant lateral displacement is due to the localization of the electromagnetic wave which can be both positive and negative depending on the incidence angle o...

How can we test the correctness of a computer implementation of an algorithm such as Gaussian elimination, or the QR algorithm for the eigenproblem? This is an important question for program libraries such as LAPACK, that are designed to run on a wide range of systems. We discuss testing based on verifying known backward or forward error properties of the algorithms, with particular reference t...

The present study aims to model systematic risk using financial and accounting variables. Accordingly, the data for 174 companies in Tehran Stock Exchange are extracted for the period of 2006 to 2016. First, the systematic risk index is estimated using the ARFIMA-FIGARCH model. Then, based on the research background, 35 affective financial and accounting variables are simultaneously used with t...

Abstract. Matrices, called ε-BD matrices, that have a bidiagonal decomposition satisfying some sign constraints are analyzed. The ε-BD matrices include all nonsingular totally positive matrices, as well as their matrices opposite in sign and their inverses. The signs of minors of ε-BD matrices are analyzed. The zero patterns of ε-BD matrices and their triangular factors are studied and applied ...

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J.H. Wilkinson put Gaussian elimination (GE) on a sound numerical footing in the 1960s when he showed that with partial pivoting the method is stable in the sense of yielding a small backward error. He also derived bounds proportional to the condition number κ(A) for the forward error ‖x − x̂‖, where x̂ is the computed solution to Ax = b. More recent work has furthered our understanding of GE, la...