The least squares (LS) estimation criterion on one hand, and the total LS (TLS), constrained TLS (CTLS) and structured TLS (STLS) criteria on the other hand, can be viewed as opposite limiting cases of a more general criterion, which we term “Extended LS” (XLS). The XLS criterion distinguishes measurement errors from modeling errors by properly weighting and balancing the two error sources. In ...

The convergence of Fourier series of trigonometric functions is easy to see, but the same question for general functions is not simple to answer. We study the convergence of Fourier series in Lp spaces. This result gives us a criterion that determines whether certain partial differential equations have solutions or not.We will follow closely the ideas from Schlag and Muscalu’s Classical and Mul...

A new criterion is introduced for comparing the convergence properties of variable metric algorithms, focusing on stepwise descent properties. This criterion is a bound on the rate of decrease in the function value at each iterative step (single-step convergence rate). Using this criterion as a basis for algorithm development leads to the introduction of variable coefficients to rescale the obj...