Embedded techniques for choosing the parameter in Tikhonov regularization

This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy principle, although no initial knowledge of the norm of the error that affects the right-hand side is assumed; an increasingly more accurate approximation of this quantity is recovered during the Arnoldi algorithm. Some theoretical estimates are derived in order to motivate our approach. Many numerical experiments, performed on classical test problems as well as image deblurring are presented

Calculation of Relaxation Spectra from Stress Relaxation Measurements

Application of stress on materials increases the energy of the system. After removal of stress, macromolecules comprising the material shift towards equilibrium to minimize the total energy of the system. This process occurs through molecular rearrangements or “relaxation” during which macromolecules attain conformations of a lower energetic state. The time, however, that is required for these rearrangements can be short or long depending on the interactions between the macromolecular species that consist the material. When rearrangements occur faster than the time of observation (experimental timescale) then molecular motion is observed (flow) and the material is regarded as viscou