/MAT3008

Numerical Analysis in Hanyang Univ

Primary LanguageJupyter Notebook

Numerical Analysis

  1. Find the machine epsilon of floating-point number

    • Method 1: using 'machar' function in NA library
    • Method 2: calculating eps by finding the largest positive integer n that satisfies 1 + 2^(-n) != 1

  2. Compare the root finding algorithms learned during the class

    in terms of their convergence speeds measured by the number of steps required to stop iterations

    To compare them,

    • Bessel Function

    • y = e^(-x)*cos(x)

    were used.

  3. Solve the linear systems or calculate inverse/determinant of an matrix using one of methods below

    • Gauss-Jordan Elimination
    • LU Decomposition
    • Singular Value Decomposition
    • Iterative Approach

  4. Programming on random number generation

    Generating psuedo-random numbers using the modular of a prime number, approximate the uniform distribution or some meaningful distribution(normal).

  5. Upscale the image using bilinear interpolation upto 3x of its size

    Using vectorization of numpy, it works much faster.

  6. Data fitting

    Implemented the General Linear Least Square