How to estimate the norm of a matrix

There is a matrix as following, \begin{eqnarray} A = \left ( \begin{array}{l} 0 \quad \quad \quad \quad \quad \quad \quad ~~ 1\\ b \quad ~~~0 \quad \quad \quad \quad \quad a\\ ab \quad ~~ b \quad ~~~0\quad \quad ~a^2\\ \vdots \quad \quad~~~ \ddots ~~\ddots \quad \vdots\\ a^{n-2}b \quad \cdots ab \quad b \quad a^{n-1} \end{array} \right ), \end{eqnarray} where $A \in \mathbf{R^n}$, $a,b \in \mathbf{R},$and $0 <a < 1$, $|b|<1$. Then how to estimate the norm or the eigenvalue of $A$ and $A^k$, where $k \in \mathbf{N^{+}}$.

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@Bo: I added some backticks around some formulas; this is sometimes necessary since two programs try to process the sourcecode, and the backticks prevent the first one (markdown) to do 'its job' where it should not (ie in ceratain formulas). In particular, lessthan-signs and double backslashes tend to cause problems. Hope I did not mess up anything in the process. @Geoff Robinson: it was not diplayed due to a formatting problem. – quid Feb 28 '12 at 11:51
@Bo: sorry for the confusion due to some parallel edits. In case you reedit please check my version. I added only six backticks three pairs: around the big formula and the two formulas containing less than signs. – quid Feb 28 '12 at 11:56
@quid: Great thanks for your help! @Geoff Robinson: now it works, and thank you ! – user21774 Feb 28 '12 at 12:10