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30.6. How many eigenvalues does 1 1 0 0 1 1 1 0 A = 0 1 2 1 0 0 1 3 have in the interval [1,2]? Work out the answer on paper by bisection, making use of the recurrence (30.9). From page 229: Introducing the shift by xI and writing p(k) = - xI), we get = (30.9) If we define p(-1-(x) = 0 and p(O)(x) = 1, then this recurrence is valid for all k = 1, 2, , m.

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