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We derive upper and lower a posteriori estimates for the maximum norm error in nite element solutions of monotone semi-linear equations. The estimates hold for Lagrange elements of any xed order, n...
Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NP-hard in general. We show here that for systems with ‘typical’/‘random’ Φ, a good approximation to the sparse...
Consider an underdetermined system of linear equations y = Ax with known n matrix A and known y. We seek the sparsest nonnegative solution, i.e. the nonnegative x with fewest nonzeros satisfying y...
Consider a d × n matrix A, with d < n. The problem of solving for x in y = Ax is underdetermined, and has many possible solutions (if there are any). In several fields it is of interest to ...
We consider linear equations y = Φα where y is a given vector in R n , Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ Rm. We suppose that the columns of Φ are normalized ...
Abstract: We consider random systems of linear equations over GF(2) in which every equation binds k variables. We obtain a precise description of the clustering of solutions in such systems. In partic...
A simple iteration methodology for the solution of a set of a linear algebraic equations is pre-sented. The explanation of this method is based on a pure geometrical interpretation and pictorial repre...
We present two new quantum algorithms. Our first algorithm is a generalization of amplitude amplification to the case when parts of the quantum algorithm that is being amplified stop at different time...
A new method for finding the exact solutions of systems of linear equations is presented. Advantage of this method is the simplicity of the procedure. There are no additional constraint conditions. Th...
In this paper, disturbed sparse linear equations over the 0-1 finite field are considered. Due to the special structure of the problem, the standard alternating coordinate method can be implemented...
In this paper, we consider solving dense linear equations on Dawning1000 by using matrix partitioning technique. Based on this partitioning of matrix, we give a parallel block LU decomposition metho...
Computational inference of haplotypes from genotypes has attracted a great deal of attention in the computational biology community recently, partially driven by the interna- tional HapMap project. In...
A method for solving nonlinear polynomial equations is given which avoids the appearance of redundant factors as in the previous characteristic set method developed by the present author. The new meth...

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