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Article: Fast preconditioned iterative methods for convolution-type integral equations
Title | Fast preconditioned iterative methods for convolution-type integral equations |
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Authors | |
Keywords | Toeplitz matrices Quadrature rules Displacement kernel Fredholm equations |
Issue Date | 2000 |
Citation | BIT Numerical Mathematics, 2000, v. 40, n. 2, p. 336-350 How to Cite? |
Abstract | We consider solving the Fredholm integral equation of the second kind with the piecewise smooth displacement kernel x(t) + ∑mj=1μjx(t - tj) + ∫τ0 k(t - s)x(s) ds = g(t), 0 ≤ t ≤ τ, where tj ∈ (-τ, τ), for 1 ≤ j ≤ m. The direct application of the quadrature rule to the above integral equation leads to a non-Toeplitz and an underdetermined matrix system. The aim of this paper is to propose a numerical scheme to approximate the integral equation such that the discretization matrix system is the sum of a Toeplitz matrix and a matrix of rank two. We apply the preconditioned conjugate gradient method with Toeplitz-like matrices as preconditioners to solve the resulting discretization system. Numerical examples are given to illustrate the fast convergence of the PCG method and the accuracy of the computed solutions. |
Persistent Identifier | http://hdl.handle.net/10722/276738 |
ISSN | 2023 Impact Factor: 1.6 2023 SCImago Journal Rankings: 1.064 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Lin, Fu Rong | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:34:30Z | - |
dc.date.available | 2019-09-18T08:34:30Z | - |
dc.date.issued | 2000 | - |
dc.identifier.citation | BIT Numerical Mathematics, 2000, v. 40, n. 2, p. 336-350 | - |
dc.identifier.issn | 0006-3835 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276738 | - |
dc.description.abstract | We consider solving the Fredholm integral equation of the second kind with the piecewise smooth displacement kernel x(t) + ∑mj=1μjx(t - tj) + ∫τ0 k(t - s)x(s) ds = g(t), 0 ≤ t ≤ τ, where tj ∈ (-τ, τ), for 1 ≤ j ≤ m. The direct application of the quadrature rule to the above integral equation leads to a non-Toeplitz and an underdetermined matrix system. The aim of this paper is to propose a numerical scheme to approximate the integral equation such that the discretization matrix system is the sum of a Toeplitz matrix and a matrix of rank two. We apply the preconditioned conjugate gradient method with Toeplitz-like matrices as preconditioners to solve the resulting discretization system. Numerical examples are given to illustrate the fast convergence of the PCG method and the accuracy of the computed solutions. | - |
dc.language | eng | - |
dc.relation.ispartof | BIT Numerical Mathematics | - |
dc.subject | Toeplitz matrices | - |
dc.subject | Quadrature rules | - |
dc.subject | Displacement kernel | - |
dc.subject | Fredholm equations | - |
dc.title | Fast preconditioned iterative methods for convolution-type integral equations | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1023/A:1022347208753 | - |
dc.identifier.scopus | eid_2-s2.0-0042185224 | - |
dc.identifier.volume | 40 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 336 | - |
dc.identifier.epage | 350 | - |
dc.identifier.isi | WOS:000086834900007 | - |
dc.identifier.issnl | 0006-3835 | - |