Many techniques of functional data analysis require choosing a measure of distance between functions, with the most common choice being L2 distance. In this article we show that using a weighted L2 distance, with a judiciously chosen weight function, can improve the performance of various statistical methods for functional data, including k-medoids clustering, nonparametric classification, and ...

the inverse problem of identifying an unknown source control param- eter in a semilinear parabolic equation under an integral overdetermina- tion condition is considered. the series pattern solution of the proposed problem is obtained by using the weighted homotopy analysis method (wham). a description of the method for solving the problem and nding the unknown parameter is derived. finally, tw...

Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...

In this article, we introduce two new generalized inverses for rectangular matrices called $W$-weighted generalized-Drazin--Moore--Penrose (GDMP) and generalized-Drazin-reflexive (GDR) inverses. The first inverse can be seen as a generalization of the recently introduced GDMP square matrix to matrix. second class contains inverse. We then exploit their various properties establish that proposed...

This paper reveals the relationship between the weighted Moore–Penrose generalized inverse and the force analysis of overconstrained parallel mechanisms (PMs), including redundantly actuated PMs and passive overconstrained PMs. The solution for the optimal distribution of the driving forces/torques of redundantly actuated PMs is derived in the form of a weighted Moore–Penrose inverse. Therefore...

This paper extends some results for the weighted Moore–Penrose inverse A+M,N in Hilbert space to the so-called weighted Minkowski inverse A⊕M,N of an arbitrary rectangular matrix A ∈ Mm,n in Minkowski spaces μ. Four methods are also used for approximating the weighted Minkowski Inverse A⊕M,N . These methods are: Borel summable, Euler–Knopp summable, Newton–Raphson and Tikhonov’s methods. c © 20...