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.

Report Date:

1981-12-01

Pagination or Media Count:

20.0

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