Resummation with Penalties

Scaling of the cost-functional and its violations are discussed with regard to their application to the summation of asymptotic truncated expansions. A new family of cost-functionals dependent only on amplitudes is considered, allowing for a continuous breaking of scaling. Cost-functionals can be a homogeneous function of the second order with respect to the scaling of all amplitudes with the same multiplicative factor. However, non-homogenous cost-functionals do violate scaling. A robust and accurate calculation of amplitudes emergent at quite a large value of the variable from the truncated series obtained for relatively small values of the variable is performed using the cost-functional technique with varying degrees of scaling violation. Various physical examples from field theory, quantum mechanics, and statistical physics are considered. Certain parallels with complex systems are noticed and discussed.