Year: 2016
Numerical Mathematics: Theory, Methods and Applications, Vol. 9 (2016), Iss. 2 : pp. 289–314
Abstract
Most current prevalent iterative methods can be classified into the socalled extended Krylov subspace methods, a class of iterative methods which do not fall into this category are also proposed in this paper. Comparing with traditional Krylov subspace methods which always depend on the matrix-vector multiplication with a fixed matrix, the newly introduced methods (the so-called (progressively) accumulated projection methods, or AP (PAP) for short) use a projection matrix which varies in every iteration to form a subspace from which an approximate solution is sought. More importantly, an accelerative approach (called APAP) is introduced to improve the convergence of PAP method. Numerical experiments demonstrate some surprisingly improved convergence behaviors. Comparisons between benchmark extended Krylov subspace methods (Block Jacobi and GMRES) are made and one can also see remarkable advantage of APAP in some examples. APAP is also used to solve systems with extremely ill-conditioned coefficient matrix (the Hilbert matrix) and numerical experiments shows that it can bring very satisfactory results even when the size of system is up to a few thousands.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2016.y14014
Numerical Mathematics: Theory, Methods and Applications, Vol. 9 (2016), Iss. 2 : pp. 289–314
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
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An orthogonally accumulated projection method for symmetric linear system of equations
Peng, WuJian
Lin, Qun
Zhang, ShuHua
Science China Mathematics, Vol. 59 (2016), Iss. 7 P.1235
https://doi.org/10.1007/s11425-016-5142-5 [Citations: 0]