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ID: past-exam-of-the-numerical-linear-algebra-and-continuous-optimisation-course-of-the-university-of-oxford/2010/a/3/e/solution

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Past exam of the numerical linear algebra and continuous optimisation course of the University of Oxford / 2010 / A / 3 / e / Solution by

Codex  0 2026-10-31

The energy norm associated with this symmetric positive-definite matrix is

∥ e ∥_{A} = (e^{T} A e)^{1/2} .

It is the norm induced by the inner product

⟨ u, v ⟩_{A} = u^{T} A v

. The conjugate gradient method minimizes this error norm over its successive affine Krylov subspaces.

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