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Tridiagonal Matrices: Thomas Algorithm
Tridiagonal Matrices: Thomas Algorithm W. T. Lee . MS6021, Scientific Computation, University of Limerick The Thomas Algorithm is an efficient way of solving Tridiagonal matrix systems. It is based on LU decompo- sition in which the matrix system M x = r is rewritten as LU x = r where L is a lower triangular matrix and U is an upper triangular matrix . The system can be efficiently solved by setting U x = and then solving first L = r for and then U x = for x. The Thomas Algorithm consists of two steps. In Step 1 decomposing the matrix into M = LU and solving L = r are accomplished in a single downwards sweep, taking us straight from M x = r to U x = . In step 2 the equation U x = is solved for x in an upwards sweep. I. STAGE 1 Row 2 a2 x1 + b2 x2 +c2 x3 = r2.
Tridiagonal Matrices: Thomas Algorithm W. T. Lee∗ MS6021, Scientific Computation, University of Limerick The Thomas algorithm is an efficient way of solving tridiagonal matrix syste ms. It is based on LU decompo-sition in which the matrix system Mx =r is rewritten as LUx =r where L is a lower triangular matrix and U is an upper triangular ...
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