Diagonal Matrix Scaling and H-Matrices

Koulaei, Mohammad H.

doi:10.12732/ijam.v28i5.1

Cited by 1 publication

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Mathematically, we thus want to consider the inverse of a block tridiagonal and block Toeplitz matrix. Theories for inverting a block tridiagonal matrix have been discussed numerous times in various contexts [167,[171][172][173][174][175][176], and very recently [178,179] the block Toeplitz structure with them. In the end, the block quasi-separable structure of the block tridiagonal and block Toeplitz Hamiltonian leads to a structured GF, which we now formulate.…”

Section: Derivation Of Cbsmentioning

confidence: 99%

See 1 more Smart Citation

A unified perspective of complex band structure: interpretations, formulations, and applications

Reuter

2016

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Complex band structure generalizes conventional band structure by also considering wavevectors with complex components. In this way, complex band structure describes both the bulk-propagating states from conventional band structure and the evanescent states that grow or decay from one unit cell to the next. Even though these latter states are excluded by translational symmetry, they become important when translational symmetry is broken via, for example, a surface or impurity. Many studies over the last 80 years have directly or indirectly developed complex band structure for an impressive range of applications, but very few discuss its fundamentals or compare its various results. In this work we build upon these previous efforts to expose the physical foundation of complex band structure, which mathematically implies its existence. We find that a material's static and dynamic electronic structure are both completely described by complex band structure. Furthermore, we show that complex band structure reflects the minimal, intrinsic information contained in the material's Hamiltonian. These realizations then provide a context for comparing and unifying the different formulations and applications of complex band structure that have been reported over the years. Ultimately, this discussion introduces the idea of examining the amount of information contained in a material's Hamiltonian so that we can find and exploit the minimal information necessary for understanding a material's properties.

show abstract

Section: Derivation Of Cbsmentioning

confidence: 99%

“…Turning now to the inversion problem (i.e., calculating the GF), there are fewer direct results. We know of only one study that has explicitly investigated the inverses of block pentadiagonal matrices [176], and it derived recurrence relations for the blocks of the inverse that are similar to Eq. (27).…”

Section: Extended Coupling Between Layersmentioning

confidence: 99%

A unified perspective of complex band structure: interpretations, formulations, and applications

Reuter

2016

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

Diagonal Matrix Scaling and H-Matrices

Cited by 1 publication

References 12 publications

A unified perspective of complex band structure: interpretations, formulations, and applications

A unified perspective of complex band structure: interpretations, formulations, and applications

Contact Info

Product

Resources

About