Linear Algebra

• Iteration methods solving of system linear equations

  • Simple iteration method
  • Gauss-Zeidel method

• QR-decomposition

  • Givens' rotation
  • Hausholder reflection

• Algorithms for finding eigenvalues

  • Simple iteration for finding maximal eigenvalue
  • QR-algorithm
  • QR-algorithm for tridiagonal matrix
  • speed up convergence QR-algorithm by Wilkinson shift

• Graph spector

  • Check graph's isomorphism
  • Building (𝑛, 𝑑, 𝛼)-expanders, finding optimal 𝛼