Archives of Acoustics, 30, 4, pp. 483-494, 2005

Uncertainty in structure dynamics resulting from matrix ill-conditioning

AGH University of Science and Technology Department of Robotics and Machine Dynamics

In the paper there are discussed certain issues concerning ill-posed problems that frequently appear in inverse problems, modal analysis, acoustics and other methods making use of matrix algebra. There is presented the mathematical definition, application of the singular value decomposition method to ill-posed problems detecting as well as a new method of improving such problems conditioning by the use of the Tikhonov regularization method. In the paper are presented some results of solution estimation of the Fredholm integral equation of the first kind that is the classical ill-posed problem. Analysis was carried out in the Matlab environment by means of the least squares and Tikhonov regularization methods for both the noiseless and noisy cases.
Keywords: ill-posed problem, ill-conditioned matrix, Tikhonov regularization method
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