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Tridiagonal Matrices

Tridiagonal Matrices. Amirkabir University of Technology-Birmingham University Bahram Taheri. Special Matrices. ( Banded Matrix). BW (Band width): HBW(Half-band width): BW = 2HBW + 1. Tridiagonal Matrices. (BW = 3).

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Tridiagonal Matrices

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  1. Tridiagonal Matrices Amirkabir University of Technology-Birmingham University Bahram Taheri

  2. Special Matrices (Banded Matrix) BW (Band width): HBW(Half-band width): BW = 2HBW + 1

  3. Tridiagonal Matrices (BW = 3) We have changed our notation for the coefficients from a’s and b’s to e’s, f’s, and g’s to avoid storing large number of useless zeros

  4. Thomas Algorithm for Solving Tridiagonal Matrices Decomposition Forward Substitution Backward Substitution Ex. Practice by hand

  5. Thomas Algoritm Pseudo-Code • Sub Thomas(e, f, g, r, n, x) • Call Decomp(e, f, g, n) • Call Substitute(e, f, g, r, n, x) • End Sub • Sub Decomp(e, f, g, n) • Dim k As Integer • For k = 2 To n • e(k) = e(k) / f(k - 1) • f(k) = f(k) - e(k) * g(k - 1) • Next k • End Sub

  6. Thomas Algorithm Pseudo-Code Continued • Sub Substitute(e, f, g, r, n, x) • Dim k As Integer • For k = 2 To n • r(k) = r(k) - e(k) * r(k - 1) • Next k • x(n) = r(n) / f(n) • For k = n - 1 To 1 Step -1 • x(k) = (r(k) - g(k) * x(k + 1)) / f(k) • Next k • End Sub

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