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"Abdelmalek, Nabih N"
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An Efficient Method for the Discrete Linear $L_1$ Approximation Problem
An improved dual simplex algorithm for the solution of the discrete linear $L_1$ approximation problem is described. In this algorithm certain intermediate iterations are skipped. This method is comparable with an improved simplex method due to Barrodale and Roberts, in both speed and number of iterations. It also has the advantage that in case of ill-conditioned problems, the basis matrix can lend itself to triangular factorization and can thus ensure a stable solution. Numerical results are given.
Journal Article
Computing the strict Chebyshev solution of overdetermined linear equations
A method for calculating the strict Chebyshev solution of overdetermined systems of linear equations using linear programming techniques is described. This method provides: (1) a way to determine, for the majority of cases, all the equations belonging to the characteristic set, (2) an efficient method to obtain the inverse of the matrix needed to calculate the strict Chebyshev solution, and (3) a way of recognizing when an element of the Chebyshev solution equals a corresponding element of the strict Chebyshev solution. As a result, in general, the computational effort is considerably reduced. Also the present method deals with full rank as well as rank deficient cases. Numerical results are given.
Journal Article
Computing the strict Chebyshev solution of overdetermined linear equations
A method for calculating the strict Chebyshev solution of overdetermined systems of linear equations using linear programming techniques is described. This method provides: (1) a way to determine, for the majority of cases, all the equations belonging to the characteristic set, (2) an efficient method to obtain the inverse of the matrix needed to calculate the strict Chebyshev solution, and (3) a way of recognizing when an element of the Chebyshev solution equals a corresponding element of the strict Chebyshev solution. As a result, in general, the computational effort is considerably reduced. Also the present method deals with full rank as well as rank deficient cases. Numerical results are given.
Journal Article
An efficient method for the discrete linear ₁ approximation problem
An improved dual simplex algorithm for the solution of the discrete linear L 1 L_1 approximation problem is described. In this algorithm certain intermediate iterations are skipped. This method is comparable with an improved simplex method due to Barrodale and Roberts, in both speed and number of iterations. It also has the advantage that in case of ill-conditioned problems, the basis matrix can lend itself to triangular factorization and can thus ensure a stable solution. Numerical results are given.
Journal Article
An efficient method for the discrete linear L1 approximation problem
NRC publication: Yes
Journal Article
Human rights at NRC
Re your July 9 editorial, \"Discrimination at NRC: Furthering the science of injustice,\" concerning the racial discrimination case against the National Research Council (NRC) by Dr. Chander Grover.
Newspaper Article