📅 2024-12-08 — Session: Matrix Analysis and Gauss-Seidel Method Review

🕒 15:05–15:15
🏷️ Labels: Matrix Analysis, Gauss-Seidel, Convergence, Linear Algebra
📂 Project: Teaching
⭐ Priority: MEDIUM

Session Goal

The goal of this session was to analyze the matrix A when ( \alpha = 0 ) and apply the Gauss-Seidel method to solve the equation ( Ax = b ), including verifying convergence conditions.

Key Activities

  • Analyzed the characteristic polynomial and eigenvalues of matrix A.
  • Applied the Gauss-Seidel method and confirmed convergence due to diagonal dominance.
  • Discussed the implications of strict diagonal dominance and its effect on convergence.
  • Computed the iteration matrix for the Gauss-Seidel method, including matrix decomposition and spectral radius calculation.
  • Handled errors during computation and retried the process to ensure accurate results.
  • Recomputed the Gauss-Seidel iteration matrix and its characteristics due to prior issues.
  • Summarized the computation process, detailing matrix splitting, iteration matrix computation, and convergence analysis.

Achievements

  • Successfully analyzed matrix A and applied the Gauss-Seidel method.
  • Identified convergence conditions and recomputed necessary matrices for accuracy.

Pending Tasks

  • Further refinement of the computation process may be needed to ensure clarity and accuracy in manual calculations.