Let A be any matrix and let A be a slight random perturbation of A. We prove that it is unlikely that A has large condition number. Using this result, we prove it is unlikely that A has large growth factor under Gaussian elimination without pivoting. By combining these results, we bound the smoothed precision needed by Gaussian elimination without pivoting. Our results improve the average-case ...

Many matrices that arise in the solution of signal processing problems have a special displacement structure. For example, adaptive filtering and direction-of-arrival estimation yield matrices of a Toeplitz type. A recent method of Gohberg, Kailath and Olshevsky (GKO) allows fast Gaussian elimination with partial pivoting for such structured matrices. In this paper, a rounding error analysis is...

Dantzig’s pivoting rule is one of the most studied pivoting rules for the simplex algorithm. Whilethe simplex algorithm with Dantzig’s rule may require an exponential number of pivoting stepson general linear programs, and even on min cost flow problems, Orlin showed that O(mn log n)Dantzig’s pivoting steps suffice to solve shortest paths problems (we denote the number of vertices<l...

The pivoting strategy of Bunch and Marcia for solving systems involving symmetric indefinite tridiagonal matrices uses two different methods for solving 2 × 2 systems when a 2 × 2 pivot is chosen. In this paper, we eliminate this need for two methods by adding another criterion for choosing a 1× 1 pivot. We demonstrate that all the results from the Bunch and Marcia pivoting strategy still hold....

We present a comparison of two approaches for Arabic-Chinese machine translation using English as a pivot language: sentence pivoting and phrase-table pivoting. Our results show that using English as a pivot in either approach outperforms direct translation from Arabic to Chinese. Our best result is the phrase-pivot system which scores higher than direct translation by 1.1 BLEU points. An error...

This paper is an attempt to exclusively focus on investigating the pivot language technique in which a bridging language is utilized to increase the quality of the Persian–Spanish low-resource Statistical Machine Translation (SMT). In this case, English is used as the bridging language, and the Persian–English SMT is combined with the English–Spanish one, where the relatively large corpora of e...

Many matrices that arise in the solution of signal processing problems have a special displacement structure. For example, adaptive filtering and direction-of-arrival estimation yield matrices of Toeplitz type. A recent method of Gohberg, Kailath and Olshevsky (GKO) allows fast Gaussian elimination with partial pivoting for such structured matrices. In this paper, a rounding error analysis is p...

In Friedmann, Hansen, and Zwick (2011) we claimed that the expected number of pivoting steps performed by the Random-Facet algorithm of Kalai and of Matoušek, Sharir, and Welzl is equal to the expected number of pivoting steps performed by Random-Facet∗, a variant of Random-Facet that bases its random decisions on one random permutation. We then obtained a lower bound on the expected number of ...

Judice and Pires developed in recent years principal pivoting methods for the solving of the so-called box linear complementarity problems (BLCPs) where the constraint matrices are restrictedly supposed to be of P–matrices. This paper aims at presenting a new principal pivoting scheme for BLCPs where the constraint matrices are loosely supposed to be row sufficient. This scheme can be applied t...

We present a pivoting algorithm for solving linear programs with linear complementarity constraints. Our method generalizes the simplex method for linear programming to deal with complementarity conditions. We develop an anticycling scheme that can verify Bouligand stationarity. We also give an optimizationbased technique to find an initial feasible vertex. Starting with a feasible vertex, our ...