What question did this study set out to answer?

To review the theoretical principles, algorithmic developments, and diverse computational applications of Chebyshev expansion algorithms and the kernel polynomial method in physics.

March 24, 2006Reviews of Modern PhysicsOpen Access

The kernel polynomial method

View Full Paper

Ask AI

Bookmark

Authors

AWAlexander WeißeMax Planck Institute for Mathematics GWGerhard WelleinFriedrich-Alexander-Universität Erlangen-Nürnberg AAAndreas AlvermannUniversität Greifswald

Discussion

Member takes

Implication

Methodological review demonstrates linear-scaling spectral calculations across quantum many-body systems, highlighting efficient numerical integration with Monte Carlo and cluster perturbation...

Key Points

To review the theoretical principles, algorithmic developments, and diverse computational applications of Chebyshev expansion algorithms and the kernel polynomial method in physics.
Evaluated polynomial expansion algorithms and kernel-based filtering techniques for computing spectral functions and correlation functions.
Analyzed resource scaling behavior as a function of system dimension across quantum models.
Examined integration strategies combining the kernel polynomial method with cluster perturbation theory and Monte Carlo frameworks.
Demonstrated that Chebyshev expansion algorithms achieve linear computational scaling with problem dimension, ensuring numerical stability for large-scale calculations.
Showed effective resolution of spectral properties across disordered systems, strongly correlated electrons, electron-phonon interactions, and quantum spin models.
Established successful embedding within advanced numerical workflows, including cluster perturbation theory and Monte Carlo simulations.

Cite This Study

Weiße et al. (2006) studied this question.

synapsesocial.com/papers/69f27cdf01adb323588dbcbe https://doi.org/10.1103/revmodphys.78.275

View Full Paper

Ask AI

Bookmark

Implication

Methodological review demonstrates linear-scaling spectral calculations across quantum many-body systems, highlighting efficient numerical integration with Monte Carlo and cluster perturbation...

The kernel polynomial method

Discussion

Member takes

Implication

Key Points

Cite This Study

The kernel polynomial method

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider