Linear Algebra and Its Applications · Problem 7.2.23

Computations with Matrices — Gilbert Strang

Mathematics · hilbert-matrix-condition-number

Problem

Compute

\lambda_{\max}

and

\lambda_{\min}

for the 8 by 8 Hilbert matrix

a_{ij} = 1/(i+j-1)

. If

Ax = b

with

\|b\| = 1

, how large can

\|x\|

be? If

b

has roundoff error less than

10^{-16}

, how large an error can this cause in

x