John Coletsos NTUA
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NUMERICAL ANALYSIS 9041   >  SUBJECT CONTENT IN OUTLINE

linear systems

  1. Computer arithmetic, approximation and errors.
  2. Gaussian Elimination.
  3. LU Factorization.
  4. Norms and Stability.
  5. Iterative Methods.
  6. Jacobi Method.
  7. Gauss-Seidel Method.
  8. Relaxation methods.

interpolation

  1. Lagrange Interpolation.
  2. Newton's Dividend Differences.
  3. Hermite Interpolation.

Numerical Differentiation and Integration

  1. Numerical Differentiation.
  2. Newton - Cotes Formulas for Numerical Integration. 
  3. Trapezoid Rule.
  4. Simpson's Rule.
  5. Composite Newton - Cotes Formulas.
  6. Error Estimates.

Non linear equations and systems

  1. Bisection Method.
  2. Regula Falsi Method.
  3. General iterative method.
  4. Newton-Raphson Method.
  5. Secant Method.
  6. Newton-Raphson Method for non linear systems.
  7. Complex Newton-Raphson Method.

least squares

  1. Least Squares Method and the Normal Equations.
 J. Coletsos 2020