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Numerical solution to a linear equation with tensor product structure
Author(s) -
Fan HungYuan,
Zhang Liping,
Chu Eric Kingwah,
Wei Yimin
Publication year - 2017
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2106
Subject(s) - mathematics , tensor product , discretization , partial differential equation , elliptic partial differential equation , numerical analysis , numerical stability , linear system , mathematical analysis , pure mathematics
Summary We consider the numerical solution of a c‐stable linear equation in the tensor product space R n 1 × ⋯ × n d, arising from a discretized elliptic partial differential equation in R d . Utilizing the stability, we produce an equivalent d‐stable generalized Stein‐like equation, which can be solved iteratively. For large‐scale problems defined by sparse and structured matrices, the methods can be modified for further efficiency, producing algorithms of O ( ∑ i n i ) + O ( n s ) computational complexity, under appropriate assumptions (with n s being the flop count for solving a linear system associated with A i − γ In i). Illustrative numerical examples will be presented.