Optimal spectral filtering in a finite subspace: a Lanczos-based implementation

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Publication Date
DOI 10.1039/A808450E
Impact Factor 3.676
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Abstract

A new method is presented to achieve optimal spectral filtering within a finite Lanczos subspace, based on a criterion of minimising the error-norm about the designated reference filtering energy. The implementation of this approach is shown to be easily achieved by a straightforward extension of the minimum residual algorithm of Paige and Saunders [SIAMJ. Numer. Anal., 1975, 12, 617]. The convergence properties of the present optimal filtering (OF) approach are compared with other direct filtering methods and also diagonalization-based methods (Lanczos and filter diagonalization) using the benchmark HO2 Hamiltonian as a test case. The OF method displays superior convergence properties to all of the other methods tested.

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Physical Chemistry Chemical Physics

Physical Chemistry Chemical Physics
CiteScore: 5.5
Self-citation Rate: 10.3%
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Physical Chemistry Chemical Physics (PCCP) is an international journal co-owned by 19 physical chemistry and physics societies from around the world. This journal publishes original, cutting-edge research in physical chemistry, chemical physics and biophysical chemistry. To be suitable for publication in PCCP, articles must include significant innovation and/or insight into physical chemistry; this is the most important criterion that reviewers and Editors will judge against when evaluating submissions. The journal has a broad scope and welcomes contributions spanning experiment, theory, computation and data science. Topical coverage includes spectroscopy, dynamics, kinetics, statistical mechanics, thermodynamics, electrochemistry, catalysis, surface science, quantum mechanics, quantum computing and machine learning. Interdisciplinary research areas such as polymers and soft matter, materials, nanoscience, energy, surfaces/interfaces, and biophysical chemistry are welcomed if they demonstrate significant innovation and/or insight into physical chemistry. Joined experimental/theoretical studies are particularly appreciated when complementary and based on up-to-date approaches.

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