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A novel recursive method for computing the null-space of random matrices of arbitrary size

Problem of finding the null-space arises times and often in many important science and engineering applications. A few of them are bioinformatics, gene expression analysis, structural analysis, computation fluid dynamics, electromagnetics, and optimization theory. Many of the existing methods rely heavily on the structure, size, and sparsity of the matrices in question and are therefore, tailored only for particular applications. Besides these, many hybrid methods have also been tried out. Instead of being helpful, they turn out to be even more complex. In this paper, we propose a novel method for computing the null-space of a matrix. The method makes no apriori assumptions as such and is applicable to purely random matrices of arbitrary size. In addition, the method is recursive in nature which provides the flexibility of finding an approximate solution whenever the cost of increase in accuracy is unjustifiable by the corresponding increase in computation time. And yet, despite all this, the method is simple, stable, and has excellent convergence properties.