Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 341 / 2 / b

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- Solution b

Solution

Algebraic stability requires

b_{i} \geq 0

and positive semidefiniteness of

M = B A + A^{T} B - b b^{T}, B = diag (b) .

The three weights are positive, but direct calculation gives

M_{11} = 2 b_{1} a_{11} - b_{1}^{2} = - \frac{1}{81} < 0.

A positive-semidefinite matrix cannot have a negative diagonal entry. Hence

the method is not algebraically stable .

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