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Positive Definite Toeplitz Completions
Author(s) -
Johnson Charles R.,
Lundquist Michael,
Nædal Geir
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007255
Subject(s) - toeplitz matrix , positive definite matrix , mathematics , levinson recursion , characterization (materials science) , conjecture , matrix (chemical analysis) , pure mathematics , combinatorics , algebra over a field , physics , chemistry , eigenvalues and eigenvectors , chromatography , quantum mechanics , optics
The problem of completing a partially prescribed Toeplitz matrix to a positive definite Toeplitz matrix is considered. The main result is a characterization of the patterns of specified entries that guarantee the existence of a positive definite Toeplitz completion of a partial positive definite Toeplitz matrix. This characterization resolves affirmatively a conjecture of C. R. Johnson and L. Rodman.