Perturbation and error analyses of partitioned LU factorization for block tridiagonal linear systems
Ukr. Mat. Zh. - 2016. - 68, № 12. - pp. 1683-1695
The perturbation and backward error analyses of the partitioned LU factorization for block tridiagonal matrices are presented. Moreover, we consider the perturbation bounds for the partitioned LU factorization for block tridiagonal linear systems. Finally, numerical examples are given to verify our results.
Ukr. Mat. Zh. - 2016. - 68, № 5. - pp. 712-720
We prove the existence of solution for the quadratic vector equation arising in Markovian binary trees. A modified Newton method for finding the minimal solution of the equation is presented. The monotone convergence of the modified Newton method is proved. Numerical experiments show the efficiency of our method.