Equations of state in solids: Fitting theoretical data, possibly including noise and jumps

An analytical equation of state is commonly fitted to the energy versus volume theoretical data to determine the equilibrium properties and obtain derivatives. A weighted average of polynomials is shown to extract optimally the information contained in the data set and provide conservative and meaningful error bars. The fitting becomes problematic when the data contains noise and small jumps. We examine some techniques that can detect and deal with those problems.