A version of the dynamical systems method (DSM) for solving ill-conditioned linear algebraic systems is studied. An a priori and an a posteriori stopping rules are justified. An iterative scheme is constructed for solving ill-conditioned linear algebraic systems.

In this letter, we present a linear-complexity encoding algorithm for any cycle GF(2) code CE(G,H). We just need to investigate the case where G is a nontrivial connected graph. If G is a tree, the only codeword is the all-zero word. If G is not a tree, first, we show that through graph analysis H can be transformed into an equivalent block-diagonal upper-triangular form simply by permuting the...

Seeking a basis for the null space of a rectangular and possibly rank deficient and ill conditioned matrix we apply randomization, augmentation, and aggregation to reduce our task to computations with well conditioned matrices of full rank. Our algorithms avoid pivoting and orthogonalization, preserve matrix structure and sparseness, and in the case of an ill conditioned input perform only a sm...

We discuss matching control laws for underactuated systems. We previously showed that this class of matching control laws is completely charactarized by a linear system of first order partial differential equations for one set of variables (λ) followed by a linear system of first order PDEs for the second set of variables (g, V). Here we derive a new first order system of partial differential e...

Seeking a basis for the null space of a rectangular and possibly rank deficient and ill conditioned matrix we apply randomization, augmentation, and aggregation to reduce our task to computations with well conditioned matrices of full rank. Our algorithms avoid pivoting and orthogonalization, preserve matrix structure and sparseness, and in the case of an ill conditioned input perform only a sm...

Seeking a basis for the null space of a rectangular and possibly rank deficient and ill conditioned matrix we apply randomization, augmentation, and aggregation to reduce our task to computations with well conditioned matrices of full rank. Our algorithms avoid pivoting and orthogonalization, preserve matrix structure and sparseness, and in the case of an ill conditioned input perform only a sm...

For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a suitable function of matrix. In this sense the method can be referred to as an iterative refinement process. Numerical experiments arising from integral equati...

Seeking a basis for the null space of a rectangular and possibly rank deficient and ill conditioned matrix we apply randomization, augmentation, and aggregation to reduce our task to computations with well conditioned matrices of full rank. Our algorithms avoid pivoting and orthogonalization, preserve matrix structure and sparseness, and in the case of an ill conditioned input perform only a sm...