<Algebraic stability> requires $b_i\geq0$ and positive semidefiniteness of
$$
\mathcal M=BA+A^TB-bb^T,\qquad B=\operatorname{diag}(b).
$$
The three weights are positive, but direct calculation gives
$$
\mathcal M_{11}=2b_1a_{11}-b_1^2=-\frac1{81}<0.
$$
A positive-semidefinite matrix cannot have a negative diagonal entry. Hence
$$
\boxed{\text{the method is not algebraically stable}.}
$$

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-341/2/b/solution