Monotone convex sequences and Cholesky decomposition of symmetric Toeplitz matrices
نویسندگان
چکیده
This paper studies off-diagonal decay in symmetric Toeplitz matrices. It is shown that if the generating sequence of the matrix is monotone, positive and convex then the monotonicity and positivity are maintained through triangular decomposition. The work is motivated by recent results on explicit bounds for inverses of triangular matrices. © 2005 Elsevier Inc. All rights reserved. AMS classification: 15A23; 15A24; 15A45; 15A09; 30C45; 47B35
منابع مشابه
Maximization for Inner Products under Quasi-monotone Constraints
This paper studies optimization for inner products of real vectors assuming monotonicity properties for the entries in one of the vectors. Resulting inequalities have been useful recently in bounding reciprocals of power series with rapidly decaying coefficients and in proving that all symmetric Toeplitz matrices generated by monotone convex sequences have offdiagonal decay preserved through tr...
متن کاملSpectral factorization of bi-infinite multi-index block Toeplitz matrices
In this paper we formulate a theory of LU and Cholesky factorization of bi-infinite block Toeplitz matrices A = (Ai−j )i,j∈Zd indexed by i, j ∈ Zd and develop two numerical methods to compute such factorizations. © 2002 Elsevier Science Inc. All rights reserved.
متن کاملCholesky Factorizations of Matrices Associated with r-Order Recurrent Sequences
In this paper we extend some results on the factorization of matrices associated to Lucas, Pascal, Stirling sequences by the Fibonacci matrix. We provide explicit factorizations of any matrix by the matrix associated with an r-order recurrent sequence Un (having U0 = 0). The Cholesky factorization for the symmetric matrix associated to Un is also obtained.
متن کاملFast direct solvers for some complex symmetric block Toeplitz linear systems
We consider the solution of a class of complex symmetric block Toeplitz linear systems, arising from integral equations problems. Algorithms that exploit the Toeplitz structure provide considerable savings on the number of arithmetic operations, compared to the classical Cholesky factorization. We propose a fast Schur algorithm adapted to the complex symmetric case. We detail blocked variants, ...
متن کاملCholesky Factorization of Semi-de nite Toeplitz Matrices
It can be shown directly from consideration of the Schur algorithm that any nn semi-deenite rank r Toeplitz matrix, T, has a factorization T = C r C T r with C r = C 11 C 12 0 0 where C 11 is r r and upper triangular. This paper explores the reliability of computing such a decomposition with O(nr) complexity using the Schur algorithm and truncating the Cholesky factor after computing the rst r ...
متن کامل