Bounds for the Error of Some Parallel Bidiagonal Solvers for Strictly Diagonal Dominant Systems

Abstract

In this paper, the numerical aspects of some methods for the solution of bidiagonal systems are analyzed. We suppose that the systems are strictly diagonal dominant. The methods analyzed are R-Cyclic Reduction, the Divide and Conquer algorithm and the Overlapped Partitions Method. In order to give completeness to the paper, we also describe the methods analyzed here. For the case of R-Cyclic Reduction and the Divide and Conquer algorithm, a unified early termination criterion is given. For the case of the Overlapped Partitions Method, a criterion for the amount of overlapping is proposed. Key words: bidiagonal systems solvers, strict diagonal dominance, parallel numerical algorithms. 1 Introduction The solution of bidiagonal systems of equations appears in different applications. For instance, when several tridiagonal systems have to be solved repeated times with the same matrix. In this case, it is convenient to find an LU decomposition of the matrix. Two bidiagonal systems have to..