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Approximate inverse based multigrid solution of large sparse linear systems

dc.contributor.advisorBenson, Maurice
dc.contributor.authorBanerjee, Rabindra Nath
dc.date.accessioned2017-06-05T19:20:26Z
dc.date.available2017-06-05T19:20:26Z
dc.date.created1988
dc.date.issued1988
dc.identifier.urihttp://knowledgecommons.lakeheadu.ca/handle/2453/1614
dc.description.abstractIn this thesis we study the approximate inverse based multigrid algorithm FAPIN for the solution of large sparse linear systems of equations. This algorithm, which is closely related to the well known multigrid V-cycle, has proven successful in the numerical solution of several second order boundary value problems. Here we are mainly concerned with its application to fourth order problems. In particular, we demonstrate good multigrid performance with discrete problems arising from the beam equation and the biharmonic (plate) equation. The work presented also represents new experience with FAPIN using cubic B-spline, bicubic B-spline and piecewise bicubic Hermite basis functions. We recast a convergence proof in matrix notation for the nonsingular case. Central to our development are the concepts of an approximate inverse and an approximate pseudo-inverse of a matrix. In particular, we use least squares approximate inverses (and related approximate pseudo-inverses) found by solving a Frobenius matrix norm minimization problem. These approximate inverses are used in the multigrid smoothers of our FAPIN algorithms.
dc.language.isoen_US
dc.subjectFAPIN (Algorithm)
dc.subjectNumerical analysis
dc.titleApproximate inverse based multigrid solution of large sparse linear systems
dc.typeThesis
etd.degree.nameMaster of Science
etd.degree.levelMaster
etd.degree.disciplineMathematical Sciences
etd.degree.grantorLakehead University


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