Tridiagonal systems of linear equations Consider the
Chapter 28, Problem 28-1(choose chapter or problem)
Tridiagonal systems of linear equations Consider the tridiagonal matrix A D 1 1000 1 2 100 0 1 2 1 0 0 0 1 2 1 000 1 2 : a. Find an LU decomposition of A. b. Solve the equation Ax D 11111 T by using forward and back substitution. c. Find the inverse of A. d. Show how, for any n n symmetric positive-definite, tridiagonal matrix A and any n-vector b, to solve the equation Ax D b in O.n/ time by performing an LU decomposition. Argue that any method based on forming A1 is asymptotically more expensive in the worst case. e. Show how, for any n n nonsingular, tridiagonal matrix A and any n-vector b, to solve the equation Ax D b in O.n/ time by performing an LUP decomposition.
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