Accession Number : ADA114494

Title :   Structure of Invertible (BI) Infinite Totally Positive Matrices.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : DE Boor,C ; Jia,Rong-qing ; Pinkus,A

PDF Url : ADA114494

Report Date : Dec 1981

Pagination or Media Count : 20

Abstract : An l subinfinity-invertible nonfinite totally positive matrix A is shown to have one and only one main diagonal. This means that exactly one diagonal of A has the property that all finite sections of A principal with respect to this diagonal are invertible and their inverses converge boundedly and entrywise to A to the -1 power. This is shown to imply restrictions on the possible shapes of such a matrix. In the proof, such a matrix is also shown to have a l subinfinity invertible LDU factorization. In addition, decay of the entries of such a matrix away from the main diagonal is demonstrated. It is also shown that a bounded sign-regular matrix carrying some bounded sequence to a uniformly alternating sequence must have all its columns in c sub o. (Author)

Descriptors :   *Matrices(Mathematics), *Approximation(Mathematics), *Least squares method, Splines, Interpolation, Finite element analysis, Stability, Linear systems

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE