/Computational-Linear-Algebra

Primary LanguageMATLAB

Computationa Linear Algebra

Develop Linear Algebra Algorithms for matrix problem solving

Coursework 1

  1. Consider Gaussian elimination with partial pivoting P A = LU for a generic square matrix
    • Compute Largest value of L.
    • Compute growth factor.
    • Find LU factorisation.
    • Parameters evaluation.
  2. Gaussian elimination with complete pivoting:
    • Solve A k x = b where k is a positive integer.
    • Solve the matrix equation AX = B, where X and B are matrices of size n × m.
  3. Solve partial differential equation governing mass transfer.

Coursework 2

  1. Rayleigh Quotient Iteration and Householder deflation method.
  2. QR iteration method.
  3. Subspace iteration and Ritz eigenvalue problem.
  4. Sensitivity of each method to numerical errors in A matrix.
  5. Accuracy and computational cost study.
  6. Eigenvalues sensitivity analysis.