Question

Let H be an upper Hessenberg matrix. Show that the flop count for computing the QR decomposition of H is O(n2), assuming that the factor Q is not assembled but left as a product of rotators.

Answer 1

Answer is explained in the attached document

Explanation:

Hessenberg matrix- it a special type of square matrix,there there are two subtypes of hessenberg matrix that is upper Hessenberg matrix and lower Hessenberg matrix.

upper Hessenberg matrix:- in this type of matrix zero entries below the first subdiagonal or in another words square matrix of n\times n is said to be in upper Hessenberg form if ai,j=0

for all i,j with i>j+1.and upper Hessenberg matrix is called unreduced if all subdiagonal entries are nonzero

lower Hessenberg matrix:- in this type of matrix zero entries upper the first subdiagonal,square matrix of n\times n is said to be in lower Hessenberg form if ai,j=0 for all i,j with j>i+1.and lower Hessenberg matrix is called unreduced if all subdiagonal entries are nonzero.