A parallel algorithm for transforming an n × n symmetric matrix to tridiagonal form is described. The algorithm implements Givens rotations on a square array of n × n processors in such a way that the transformation can be performed in time O(n log n). The processors require only nearest-neighbor communication. The reduction to tridiagonal form could be the first step in the parallel solution o...

In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly perturbed delay differential equations is modified by approximating the term containing negative shift using Taylor series expansion. After approximating the coefficient of the second derivative of the...

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respec...

Ve consider tl1e problem or re<:eH18l.r11dir1g Jacobi rnatric:e8 a.rid real symmetric: arrow ma.I.rices from two cigcnpairs. ,'\lgoritl1rn8 ror solving l.licsc i11vcr8c problem;; are presented. \Ve show that there are rea;;onable condition;;, under which this reconstruction is always possible. }foreover, it is ;;,een that in certain cases reconstruction can proceed with little or no cancellatio...

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respec...

In this paper we study the condition number of linear systems, the condition number of matrix inversion, and the distance to the nearest singular matrix, all problems with respect to normwise structured perturbations. The structures under investigation are symmetric, persymmetric, skewsymmetric, symmetric Toeplitz, general Toeplitz, circulant, Hankel, and persymmetric Hankel matrices (some resu...