Kavahn's Notes

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Sep 12, 20243 min read

Part (a): Best-Fit Cubic Polynomial:
  • Normal System Equation Matrix (A^T A):
  • Vector (A^T \mathbf{b}):
  • Coefficients of the best-fit cubic polynomial:
  • Resulting cubic polynomial:
Part (b): Matrix Computations:

  • Matrix ( A ):

  • Matrix ( A^T A ):

  • Eigen decomposition:

    • Matrix ( P ):

    • Matrix ( D ):

  • Orthogonality check ( ( P^T P ) ):

  • Singular Value Decomposition:

    • Matrix ( U ):

    • Matrix ( S ):

    • Matrix ( V ):

  • Comparison of ( S^T S ) and ( D ):

  • Comparison of ( V ) and ( P ):

    • Matrix ( V ):

    • Matrix ( P ):

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