Structure of Invertible (BI) Infinite Totally Positive Matrices.

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)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1981
Accession Number
ADA114494

Entities

People

  • A. Pinkus
  • C. De Boor
  • Rong-qing Jia

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Contracts
  • Convergence
  • Difference Equations
  • Equations
  • Identities
  • Inequalities
  • Interpolation
  • Intervals
  • Mathematics
  • Military Research
  • North Carolina
  • Numerical Analysis
  • Sequences
  • Smoothing (Mathematics)
  • United States
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

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  • Operations Research