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The Solution of Certain Banded Systems of Linear Equations Using the Folding Algorithm
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1976
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Numerical AnalysisFolding AlgorithmEngineeringNumerical ComputationGaussian EliminationCertain Banded SystemsInverse ProblemsMatrix MethodMatrix TheoryComputational MechanicsMatrix AnalysisOrdinary Differential EquationsBanded SystemNumerical Method For Partial Differential EquationLinear Equations
The problem of solving a banded system of linear equations Ax = b occurs frequently in the numerical solution of partial and ordinary differential equations. In the case when the matrix A is banded with semi-bandwidth p and the elements satisfy the relationship ai, j = an−i+1, n−j+1, simple techniques of folding enable a more compact version of Gaussian elimination to be constructed which possess advantages of efficiency and accuracy.