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The use of high order fully implicit Runge-Kutta methods is of significantimportance in the context of the numerical solution of transient partialdifferential equations, in particular when solving large scale problems due tofine space resolution with many millions of spatial degrees of freedom and longtime intervals. In this study we consider strongly A-stable implicitRunge-Kutta methods of arbitrary order of accuracy, based on Radau quadratures,for which efficient preconditioners have been introduced. A refined spectralanalysis of the corresponding matrices and matrix-sequences is presented, bothin terms of localization and asymptotic global distribution of the eigenvalues.Specific expressions of the eigenvectors are also obtained. The given studyfully agrees with the numerically observed spectral behavior and substantiallyimproves the theoretical studies done in this direction so far. Concludingremarks and open problems end the current work, with specific attention to thepotential generalizations of the hereby suggested general approach.

Fine spectral analysis of preconditioned matrices and matrix-sequences  arising from stage-parallel implicit Runge-Kutta methods of arbitrarily high  order