Numerical Study of Some Systems of Linear Algebraic Equations with Noise Related to Boundary-value Problems for Laplace

Citation:
Sweilam, N. H., W. Mahmoud, and E. K. Rawy, "Numerical Study of Some Systems of Linear Algebraic Equations with Noise Related to Boundary-value Problems for Laplace", Studies in Nonlinear Sciences 2 (2): 60-69 (2011), 2011.

Abstract:

We investigate two stable methods for solving the system of linear algebraic equations arising
from plane, singular boundary-value problems for Laplace’s equation for rectangular domains [1, 21]. The
dynamical systems method and the variational regularization method are applied to derive stable solutions
for these systems, and the results are compared with those obtained from the QR-factorization technique
contaminated with noise. The results put in evidence the difficulties that may arise from the use of the QRfactorization
method due to instability.

Notes:

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