In this paper, we present a new sixth-order iterative method for solving nonlinear systems and prove a local convergence result. The new method requires solving five linear systems per iteration. An important feature of the new method is that the LU (lower upper, also called LU factorization) decomposition of the Jacobian matrix is computed only once in each iteration. The computational efficie...

Permuting the rows and columns of a sparse matrix can dramatically reduce the memory requirements of a subsequently computed LU factorization. A perfect elimination matrix is one whose rows and columns can be permuted so that its LU factors require no additional space on top of that required by the original matrix. An implemention of an O(n) algorithm, presented in [6], for determining whether ...

Abstract Block low-rank (BLR) matrices possess a blockwise property that can be exploited to reduce the complexity of numerical linear algebra algorithms. The impact these approximations on stability algorithms in floating-point arithmetic has not previously been analysed. We present rounding error analysis for solution system by LU factorization BLR matrices. Assuming stable pivoting scheme is...

An implicit characteristic-based approach for numerical solution of Maxwell’s time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the...