A PARALLEL DIVIDE AND CONQUER ALGORITHM FOR NON SYMMETRIC TRIDIAGONAL TOEPLITZ SYSTEMS USING CONJUGATE GRADIENT
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Parallel algorithm for tridiagonal Toeplitz systems; a numerical computing contribution in its own domain.
This develops an algorithm for solving mathematical systems, not a study of research methods or practice.
Numerical linear-algebra algorithm paper; computational mathematics, not research as object.
Abstract
Abstract In this paper, we consider the application of the conjugate gradient method specifically to solve non symmetric systems which are large, tridiagonal and Toeplitz. Under the condition that the system is diagonally dominant, one can pre-multiply the system by the transpose of the coefficient matrix and take advantage of the structure of the new coefficient matrix to perturb and factor it. This allows us to divide the task of solution containing pairs of tridiagonal, symmetric and Toeplitz systems and to solve the pairs of systems using a parallel implementaton of congujate gradient. Final corrections, to account for the perturbations, provide a numerical approximation to the solution.
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The record
- Venue
- Parallel algorithms and applications
- Topic
- Matrix Theory and Algorithms
- Field
- Computer Science
- Canadian institutions
- University of New Brunswick
- Funders
- —
- Keywords
- Tridiagonal matrixToeplitz matrixConjugate gradient methodMathematicsTransposeDiagonalDivide and conquer algorithmsTridiagonal matrix algorithmBiconjugate gradient methodBand matrixMatrix (chemical analysis)Biconjugate gradient stabilized methodComplex conjugatePositive-definite matrixAlgorithmSymmetric matrixApplied mathematicsConjugate residual methodComputer scienceMathematical analysisSquare matrixPure mathematicsGradient descentGeometryEigenvalues and eigenvectors
- Has abstract in OpenAlex
- yes