Sentence examples for matrix extension with from inspiring English sources

Moreover, our results cover the case for paraunitary matrix extension with symmetry (i.e., the given pair satisfies P="P˜).

As an application of our general results on biorthogonal matrix extension with symmetry, we obtain a satisfactory algorithm for constructing univariate biorthogonal multiwavelets with symmetry for any dilation factor d from a given pair of biorthogonal d-refinable function vectors with symmetry.

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).

Using our matrix extension algorithm, any existing VCS with random-looking shares can be easily modified to utilize meaningful shares.

In this paper, we start with a more concise derivation of matrix extension in the ECVS model.

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.

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.

I signed an extension with the Diamondbacks.

Attach the extension with a latch hook.

Pairwise alignments for comparison of fly and human proteins were generated with the Needleman-Wunsch global alignment algorithm using the PAM250 scoring matrix with a gap extension penalty of 0.5 and an open gap penalty of 10.