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- W235721510 abstract "The conjugate gradient and the Lanczos method are the powerful tools for solving an eigenproblem with sparse sets and for solving a sparse linear system of equations, with a symmetric positive definte matrix. The equivalence in the exact computation of the Conjugate Gradient(CG) method and the Lanczos tridiagonalization scheme has been well known. These algorithms suffer from the round-off errors, which cause the derived vectors to lose their mutual orthogonality. In this paper, we consider the data flow analysis of both methods to investigate any underlying the mechanism for the propagation of loss of orthogonality, using the geometric representation of inner products on recurrence relation. We also give some numerical experiments." @default.
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- W235721510 date "1986-01-01" @default.
- W235721510 modified "2023-09-27" @default.
- W235721510 title "Data Flow Analysis of Orthogonal Properties on the Conjugate Gradient and the Lanczos Algorithm" @default.
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- W235721510 doi "https://doi.org/10.1016/b978-0-444-70067-4.50018-2" @default.
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