In our previous work, an effective preconditioning scheme that is based upon constructing least-squares approximation cardinal basis functions (ACBFs) from linear combinations of the RBF-PDE matrix elements has shown very attractive numerical results. The preconditioner costs O(N2) flops to set up and O(N) storage. The preconditioning technique is sufficiently general that it can be applied to ...

The Least Mean Square (LMS) algorithm, introduced by Widrow and Hoff in 1959 [12] is an adaptive algorithm, which uses a gradient-based method of steepest decent [10]. LMS algorithm uses the estimates of the gradient vector from the available data. LMS incorporates an iterative procedure that makes successive corrections to the weight vector in the direction of the negative of the gradient vect...

Partial least square (PLS) analysis is the most favourite tool in chemometrics to develop calibration models. PLS technique allows us decipher even complex systems by analysing all variables instead of looking at them one a time. not only capture maximum variation associated with predictor (i.e. spectra) and predicted concentration) but also maximises correlation between them. The present artic...

We study the minimal density of letters in infinite square-free words. First, we give some definitions of minimal density in infinite words and prove their equivalence. Further, we propose a method that allows to strongly reduce an exhaustive search for obtaining lower bounds for minimal density. Next, we develop a technique for constructing square-free morphisms with extremely small density fo...

The Least Mean Square (LMS) algorithm, introduced by Widrow and Hoff in 1959 [12] is an adaptive algorithm, which uses a gradient-based method of steepest decent [10]. LMS algorithm uses the estimates of the gradient vector from the available data. LMS incorporates an iterative procedure that makes successive corrections to the weight vector in the direction of the negative of the gradient vect...