Sentence examples for matrix extension problem from inspiring English sources

In this paper, we investigate the biorthogonal matrix extension problem with symmetry and its application to construction of biorthogonal multiwavelets.

We satisfactorily solve the biorthogonal matrix extension problem with symmetry and provide a step-by-step algorithm for constructing the desired pair of extension matrices (Pe,˜Pe) from the given pair of matrices (P,˜P).

Given a pair of biorthogonal matrices (P,˜P), the biorthogonal matrix extension problem is to find a pair of extension matrices (Pe,˜Pe) of Laurent polynomials with symmetry such that the submatrix of the first r rows of Pe,˜Pe is the given matrix P,˜P, respectively; Pe and ˜Pe are biorthogonal satisfying PeP˜e⋆="Is; and Pe and ˜Pe have the same compatible symmetry.

In this paper, we provide an efficient algorithm for computing its solution which compares very favorably with existing algorithms designed for positive definite matrix extension problems.

This is the extension problem.

(This can be called "the extension problem").

In the (L^2) extension problem, one would like to make the extension as small as possible.

In the paper, we consider the extension problem (1.2).

A concrete analysis on the coverage extension problem is proposed.

There are yet more extension problems for the likeness program.

Extension problems for additional practice are also included.