The LU-factorization of totally positive matrices
نویسندگان
چکیده
منابع مشابه
THE USE OF SEMI INHERITED LU FACTORIZATION OF MATRICES IN INTERPOLATION OF DATA
The polynomial interpolation in one dimensional space R is an important method to approximate the functions. The Lagrange and Newton methods are two well known types of interpolations. In this work, we describe the semi inherited interpolation for approximating the values of a function. In this case, the interpolation matrix has the semi inherited LU factorization.
متن کاملLU decomposition of totally nonnegative matrices
A uniqueness theorem for an LU decomposition of a totally nonnegative matrix is obtained.
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We give a review of the theory of factorization of block Toeplitz matrices of the type T = (Ti−j)i,j∈Zd , where Ti−j are complex k × k matrices, in the form T = LDU, with L and L−1 lower block triangular, U and U−1 upper block triangular Toeplitz matrices, and D a diagonal matrix function. In particular, it is discussed how decay properties of Ti a ect decay properties of L, L−1, U , and U−1. W...
متن کاملthe use of semi inherited lu factorization of matrices in interpolation of data
the polynomial interpolation in one dimensional space r is an important method to approximate the functions. the lagrange and newton methods are two well known types of interpolations. in this work, we describe the semi inherited interpolation for approximating the values of a function. in this case, the interpolation matrix has the semi inherited lu factorization.
متن کاملImmanants of Totally Positive Matrices Are Nonnegative
If/ is an irreducible character of Sn, these functions are known as immanants; if/ is an irreducible character of some subgroup G of Sn (extended trivially to all of Sn by defining /(vv) = 0 for w$G), these are known as generalized matrix functions. Note that the determinant and permanent are obtained by choosing / to be the sign character and trivial character of Sn, respectively. We should po...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1973
ISSN: 0024-3795
DOI: 10.1016/0024-3795(73)90039-6