1. The problem describes a cyclic tridiagonal matrix $A$ defined by entries involving $\lambda_i$ and $\mu_i$ which depend on the mesh sizes $h_i$ of a partition $a = x_0 < x_1 < \cdots < x_n = b$. 2. We have vectors $y = [y_0, \ldots, y_n]^T$ and $s = [s_1, \ldots, s_n]^T$ where $s_i = g'(x_i)$ are derivatives at the nodes, and the system $As = b$ is perturbed to $A\hat{s} = b + e$ with error vector $e$. 3. The problem gives bounds on the norms of $A$, $A^{-1}$, and the relative error $\frac{\|e\|_p}{\|b\|_p} \leq 0.10$. 4. We want to estimate the relative errors in the solution $s$, i.e., $$\frac{\|\hat{s} - s\|_\infty}{\|s\|_\infty} \quad \text{and} \quad \frac{\|\hat{s} - s\|_1}{\|s\|_1}.$$ 5. Using the standard perturbation bound for linear systems: $$\frac{\|\hat{s} - s\|_p}{\|s\|_p} \leq \|A^{-1}\|_p \|A\|_p \frac{\|e\|_p}{\|b\|_p}.$$ 6. For $p=\infty$, given $\|A\|_\infty = 3$, $\|A^{-1}\|_\infty \leq 10$, and $\frac{\|e\|_\infty}{\|b\|_\infty} \leq 0.10$, we get: $$\frac{\|\hat{s} - s\|_\infty}{\|s\|_\infty} \leq 10 \times 3 \times 0.10 = 3.0.$$ 7. For $p=1$, given $\|A\|_1 \leq \frac{10}{3}$, $\|A^{-1}\|_1 \leq \frac{3}{2}$, and $\frac{\|e\|_1}{\|b\|_1} \leq 0.10$, we get: $$\frac{\|\hat{s} - s\|_1}{\|s\|_1} \leq \frac{3}{2} \times \frac{10}{3} \times 0.10 = 0.5.$$ 8. Interpretation: The relative error in the infinity norm can be as large as 3 times the relative error in $b$, indicating potential sensitivity in the worst-case component. The relative error in the 1-norm is smaller, at most 0.5 times the relative error in $b$, indicating better average stability. 9. This analysis helps understand the stability of the cyclic tridiagonal system solution under perturbations. Final answers: $$\frac{\|\hat{s} - s\|_\infty}{\|s\|_\infty} \leq 3.0, \quad \frac{\|\hat{s} - s\|_1}{\|s\|_1} \leq 0.5.$$