Matricial Baxter's theorem with a Nehari sequence

Kasahara, Yukio; Bingham, Ν. H.

doi:10.1002/mana.201700147

Cited by 4 publications

(2 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The conditions (1.2) and (1.6) also imply that all of {a k }, {c k }, {ã k } and {c k } belong to ℓ d×d 1+ . See Theorem 3.3 and (3.3) in [12]; see also Theorem…”

Section: Strong Convergence Results For Toeplitz Systemsmentioning

confidence: 99%

Explicit formulas for the inverses of Toeplitz matrices, with applications

Inoue¹

2021

Preprint

View full text Add to dashboard Cite

We derive explicit formulas for the inverses of truncated block Toeplitz matrices that have a positive Hermitian matrix symbol with integrable inverse. The main ingredients of the formulas are the Fourier coefficients of the phase function attached to the symbol. The derivation of the formulas involves the dual process of a stationary process that has the symbol as spectral density. We illustrate the usefulness of the formulas by two applications. The first one is a strong convergence result for solutions of Toeplitz systems. The second application is closed-form formulas for the inverses of truncated block Toeplitz matrices that have a rational symbol. The significance of the closed-form formulas is that they provide us with a linear-time algorithm to compute the solutions of corresponding Toeplitz systems.

show abstract

“…The conditions (1.2) and (1.6) also imply that all of {a k }, {c k }, {ã k } and {c k } belong to ℓ d×d 1+ . See Theorem 3.3 and (3.3) in [12]; see also Theorem…”

Section: Strong Convergence Results For Toeplitz Systemsmentioning

confidence: 99%

Explicit formulas for the inverses of Toeplitz matrices, with applications

Inoue¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…and also [11]. Recently, the authors [13] proved Baxter's theorem which asserts that γ is summable if and only if so is α.…”

Section: Introductionmentioning

confidence: 99%

Coefficient stripping in the matricial Nehari problem

Kasahara

Bingham

2017

Journal of Approximation Theory

Self Cite

View full text Add to dashboard Cite

show abstract

Explicit formulas for the inverses of Toeplitz matrices, with applications

Inoue

2022

Probab. Theory Relat. Fields

View full text Add to dashboard Cite

We derive novel explicit formulas for the inverses of truncated block Toeplitz matrices that correspond to a multivariate minimal stationary process. The main ingredients of the formulas are the Fourier coefficients of the phase function attached to the spectral density of the process. The derivation of the formulas is based on a recently developed finite prediction theory applied to the dual process of the stationary process. We illustrate the usefulness of the formulas by two applications. The first one is a strong convergence result for solutions of general block Toeplitz systems for a multivariate short-memory process. The second application is closed-form formulas for the inverses of truncated block Toeplitz matrices corresponding to a multivariate ARMA process. The significance of the latter is that they provide us with a linear-time algorithm to compute the solutions of corresponding block Toeplitz systems.

show abstract

Matricial Baxter's theorem with a Nehari sequence

Cited by 4 publications

References 16 publications

Explicit formulas for the inverses of Toeplitz matrices, with applications

Explicit formulas for the inverses of Toeplitz matrices, with applications

Coefficient stripping in the matricial Nehari problem

Explicit formulas for the inverses of Toeplitz matrices, with applications

Contact Info

Product

Resources

About