Fixed-point iteration for relaxation spectrum from dynamic mechanical data

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Abstract
An algorithm was developed for the continuous spectrum of linear viscoelasticity. The algorithm is free from the possibility of negative relaxation intensity whereas most previous algorithms suffer from the problem. The algorithm is not only simpler than the nonlinear regularization of Honerkamp and Weese [Rheol. Acta 32, 65–73 (1993)] but is also as accurate as the nonlinear regularization. The basic concept of the algorithm is to use a fixed-point iteration, which transforms the initial spectrum to a new one that is closer to the least-square solution. The iteration algorithm regularizes the errors in data in a different manner of conventional regularization.An algorithm was developed for the continuous spectrum of linear viscoelasticity. The algorithm is free from the possibility of negative relaxation intensity whereas most previous algorithms suffer from the problem. The algorithm is not only simpler than the nonlinear regularization of Honerkamp and Weese [Rheol. Acta 32, 65–73 (1993)] but is also as accurate as the nonlinear regularization. The basic concept of the algorithm is to use a fixed-point iteration, which transforms the initial spectrum to a new one that is closer to the least-square solution. The iteration algorithm regularizes the errors in data in a different manner of conventional regularization.

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