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Related Experiment Video

Updated: Jun 3, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Novel algorithm of large-scale simultaneous linear equations.

T Fujiwara1, T Hoshi, S Yamamoto

  • 1Center for Research and Development of Higher Education, The University of Tokyo, Bunkyo-ku, Tokyo, 113-8656, Japan.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 10, 2011
PubMed
Summary
This summary is machine-generated.

We present efficient methods for solving large linear equations in electronic structure calculations. Our shifted conjugate orthogonal conjugate gradient (COCG) method significantly reduces computational costs for complex models.

Related Experiment Videos

Last Updated: Jun 3, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Area of Science:

  • Computational physics
  • Quantum chemistry
  • Materials science

Background:

  • Solving large-scale simultaneous linear equations is crucial for electronic structure calculations.
  • Existing methods face computational challenges in one-electron and many-electron theories.
  • Efficient algorithms are needed for accurate modeling of complex systems.

Purpose of the Study:

  • To review recently developed methods for solving large-scale linear equations.
  • To present applications of these methods in electronic structure calculations.
  • To highlight techniques that reduce computational cost.

Main Methods:

  • Shifted conjugate orthogonal conjugate gradient (COCG) method based on Krylov subspace.
  • Development of a shift equation and seed switching method to optimize calculations.
  • Application of these methods to nano-scale silicon crystals and the double orbital extended Hubbard model.

Main Results:

  • The shifted COCG method offers an efficient approach to solving large linear systems.
  • The shift equation and seed switching techniques substantially decrease computational expense.
  • Successful application to complex systems like nano-scale Si crystals and the extended Hubbard model.

Conclusions:

  • The developed methods provide a computationally efficient pathway for electronic structure calculations.
  • These advancements are applicable to both one-electron and many-electron theories.
  • The techniques enable more feasible simulations of advanced materials and models.