(a) Write a program for n à n matrices that prints every step. Apply it to the...
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(b) Experiment in (a) with shifting. Which shift do you find optimal?
(c). Consider
and take
Show that for q = 0, δ = 1 all steps and the eigenvalues are ±1, so that the interval [q - δ, q + δ] cannot be shortened (by omitting ±1) without losing the inclusion property. Experiment with other x0s.
(d) Find a (nonsymmetric) matrix for which δ in (2) is no longer an error bound.
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