期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 110, 期 46, 页码 18368-18373出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1318679110
关键词
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资金
- National Science Foundation [DMR-1106024]
- US Department of Energy (DOE) [DE-AC02-05CH11231]
- US DOE [DE-FG02-05ER25710]
- Office of Naval Research [N00014-11-1-719]
- Direct For Mathematical & Physical Scien [1106024] Funding Source: National Science Foundation
- Division Of Materials Research [1106024] Funding Source: National Science Foundation
This article describes a general formalism for obtaining spatially localized (sparse) solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrodinger's equation in quantum mechanics. Sparsity is achieved by adding an L-1 regularization term to the variational principle, which is shown to yield solutions with compact support (compressed modes). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size.
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