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Abstract: We address design of a numerical algorithm for solving the linear system arising in numerical inversion of Laplace transforms in real case [L. D’Amore, A. Murli, Regularization of a Fourier series method for the Laplace transform inversion with real data, Inverse Problems 18 (2002) 1185–1205]. The matrix has a condition number that grows almost exponentially and the singular values decay gradually towards zero. In such a case, because of this intrinsic strong instability, the main difficulty of any numerical computation is the ability of discovering at run time, only using data, what is the maximum attainable accuracy on the solution. In this paper, we use GMRES with the aim of relating the current residuals to the maximum attainable accuracy of the approximate solution by using a suitable stopping rule. We prove that GMRES stops after, at most, as many iterations as the number of the largest eigenvalues (compared to the machine epsilon). We use a split preconditioner that symmetrically precondition the initial system. By this way, the largest eigenvalue dynamically provides the estimate of the condition number of the matrix. [Copyright &y& Elsevier]

Calcinosis is a typical feature of systemic sclerosis (SSc) and can be found in many different tissues including the superficial soft tissues, periarticular structures, muscles, and tendons. It can also provoke erosive changes on bones. Investigation is conducted most often with plain radiographs. However, when a more detailed assessment is necessary, multidetector computed tomography (MDCT) is helpful owing to its multiplanar reformat (MPR) ability. The purpose of this review is to provide an overview of the various appearances of calcinosis in SSc patients as visualized at MDCT. [Copyright &y& Elsevier]