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Kernel polynomial approximations for densities of states and spectral functions. (English) Zbl 0863.65080
Efficient and numerically stable calculations of the properties of very large Hamiltonians are facilitated by the use of Chebyshev polynomial expansions and approximations. An optimal kernel polynomial (Jackson) is found that enforces the non-negativity of the density of states, preserves normalization and gives the best corresponding energy resolution. The relationship to classical uniform approximation theory is noted. Other kernels and methods in use are discussed and compared. The kernel polynomial method is demonstrated for electronic structure and magnetic susceptibility calculations. The use of Chebyshev polynomial approximation of Fermi projection operators is also proposed.

MSC:
65Z05 Applications to the sciences
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
82B10 Quantum equilibrium statistical mechanics (general)
35Q40 PDEs in connection with quantum mechanics
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