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Computational Methods

Task 1

  • source file: conds.py
  • tests:
    • m1, 1, -1
    • m2, 1, 1
    • m3, 1, -1
    • m4, 0, 0
    • hilbert, 3, -1
  • conclusions:
    • m1, m3, hilbert => grand conds lead to grand errors
    • m2 => method inaplicable for identity matrix
    • m4 => method inaplicable for some tridiagonal matrix

Task 2

  • source files:
    • lu_decomposition.py
    • regularisation.py
  • conclusions:
    • conds change during LU decomposition
    • best alphas in regularisation do not match

Task 3

  • source file: qr_decomposition.py
  • conclusion: sometimes cond_s grow up, but other conds always go down

Task 5

  • source file: eigenvalue.py
  • conclusions:
    • the less is the epsilon the more iterations are needed
    • scal_method is better

Task 6

  • source file: jacobi.py
  • conclusions:
    • The more is precision, the more iterations are needed.
    • Found eigenvalues are in Gershgorin circles.

Task 7

  • source file: grid_method.py
  • conclusions are obvious

Task 8

  • source file: galerkin.py
  • conclusion: the bigger is N the better is solution

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