Consider the tridiagonal matrix a. Find an LU decomposition of A. b.?Solve the equation?Ax?=(1 1 1 1
Question:
Consider the tridiagonal matrix
a. Find an LU decomposition of A.
b.?Solve the equation?Ax?=(1 1 1 1 1)T by using forward and back substitution.
c.?Find the inverse of?A.
d.?Show how, for any?n?נn?symmetric positive-definite, tridiagonal matrix?A?and any?n-vector?b, to solve the equation?Ax?=?b?in?O(n)?time by performing an LU decomposition. Argue that any method based on forming?A-1 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 = b in O(n) time by performing an LUP decomposition.
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a An LU decomposition of a tridiagonal matrix can be performed by using the Thomas algorithm which i...View the full answer
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Related Book For 
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
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