The Bidiagonal Factorizations Of Certain Sign Regular Matrices

In this paper we mainly do some research about two problems: frstly wediscuss the characterizations and bidiagonal decompositions of certain sign reg-ular matrices and then we study several decompositions of almost strictly signregular matrices including QR and LDU fractions.The structure of this paper is as follows:In Chapter1we briefly introduce the relative background and the presentresearch situation of sign regular matrices. In addition we introduce the mainwork of this article.In Chapter2we introduce some defnitions sign and some nature of signregular matrices. At the same time we provide some important lemmas.In Chapter3The bidiagonal factorizations of matrix A∈Rn×nwith signa-ture=(i) which satisfes thatwill be discussed. Therefore then it is not difcult to fnd that LDU and bidiag-onal factorizations of nonsingular totally positive matrices are only the corollaryof the proposition.In Chapter4we research the bidiagonal decompositions of the nonsingularalmost strictly sign regular matrix specially last we provide the QR factorization of almost strictly sign regular matrix.In Chapter5we obtain algorithms of the bidiagonal decompositions of thenonsingular almost strictly totally positive matrix. At the same time we showthe applications of bidiagonal decompositions to compute with high relative ac-curacy their singular values eigenvalues inverses or their LDU factorization.