Recently Fernando successfully resurrected a classical method for computing eigen vectors which goes back to the times of Cauchy This algorithm has been in the doldrums for nearly fty years because of a fundamental di culty highlighted by Wilkinson The algorithm is based on the solution of a nearly homogeneous system of equations J I z k ek zk for the approximate eigenvector z where is an eigen...

INTRODUCTION Segmental ureterectomy with preservation of the kidney is a treatment option for the low grade urothelial carcinoma (LG-UC) in distal ureter that is not a candidate for endoscopic resection. Laparoscopic distal ureterectomy (LDU) with ureteral reimplantation is common in benign conditions (stenosis, iatrogenic lesion, endometriosis). However, it has been hardly described in maligna...

We show that the generating function of the symmetric group with respect to five particular statistics gives rise to an exponential Riordan array, whose inverse is the coefficient array of the associated orthogonal polynomials. This also provides us with an LDU factorization of the Hankel matrix of the associated moments.

In this paper we give a combinatorial proof of an addition formula for weighted partial Motzkin paths. The addition formula allows us to determine the LDU decomposition of a Hankel matrix of the polynomial sequence defined by weighted partial Motzkin paths. As a direct consequence, we get the determinant of the Hankel matrix of certain combinatorial sequences. In addition, we obtain an addition...

General sparse elimination is designed to take maximum advantage of the sparsity of an N ×N matrix A. Only the nonzeros of A are stored, along with some extra integer overhead to identify the nonzero matrix elements. This extra integer storage may be avoided for the triangular factors generated by an LDU decomposition, generally without increasing the order of complexity. In addition to permane...

An efficient method for the computation to high relative accuracy of the LDU decomposition of an n × n row diagonally dominant M–matrix is presented, assuming that the off–diagonal entries and row sums are given. This method costs an additional O(n) elementary operations over the cost of Gaussian elimination, and leads to a lower triangular, column diagonally dominant matrix and an upper triang...

In this work we consider the approximate inverse preconditioners AISM based on the Sherman-Morrison formula [1]. We will show some of theoretical properties of the factors of AISM in function of the value of parameter s considered in the decomposition. In particular, we will show that one of the factors hides a scaled factor of the standard incomplete LDU decomposition of the system matrix A. T...