Least-squares approximation of an improper correlation matrix by a proper one

Least-squares Approximation of an Improper Correlation Matrix by a Proper One

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based upon a solution for Mosier's oblique Procrustes rotation problem offered by ten Berge and Nevels. A necessary and sufficient condition is given for a solution to yield the unique global minimum of the least-squares fu...

Least Squares Approximation by One-Pass Methods with Piecewise Polynomials

We propose several one-pass methods for data fitting in which a piecewise polynomial is used as an approximating function. The polynomial pieces are calculated step-by-step by the method of least squares as the data is -----------,scaIIIIed umy-once-from the begimring La tIre end. To calculate the least squares fitting in each step, we use three classes of data, namely: the data in the current ...

Least-squares approximation by a tree distance

Let T be a tree with vertex set V (T ) = {1, . . . , n} and with a positive weight associated with each edge. The tree distance between i and j is the weight of the ij-path. Given a symmetric, positive real valued function on V (T )×V (T ), we consider the problem of approximating it by a tree distance corresponding to T, by the least-squares method. The problem is solved explicitly when T is a...

Least Squares Approximation

In many applications we want to find an approximation for a function, for example for differential equations. Example problem: We want to understand how a calculator or computer can evaluate sinx for a given value x. The processor can essentially only perform addition, multiplication, division. Therefore we can try to approximate the function with a polynomial. We use the notation Pn for polyno...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations