numerical_methods.interpolation package¶
Submodules¶
numerical_methods.interpolation.forward_elimination_non_null module¶
- numerical_methods.interpolation.forward_elimination_non_null.forward_elimination_non_null(A: list[list[float]], b: list[float], n: int) list[float] | int[source]¶
Perform Gaussian elimination with a non-zero pivot constraint and solve the system using back substitution.
This function assumes that no pivot will be zero (i.e., A[k][k] ≠ 0). Otherwise, it prints an error.
- Parameters:
A (list[list[float]]) – Coefficient matrix of size n x n.
b (list[float]) – Right-hand side vector.
n (int) – Number of equations/unknowns.
- Returns:
Solution vector X if successful, or 0 if a zero pivot is encountered.
- Return type:
list[float] | int
numerical_methods.interpolation.lagrange_interpolation module¶
- numerical_methods.interpolation.lagrange_interpolation.lagrange_interpolation(n: int, x: float, points: list[list[float]]) None[source]¶
Evaluate the Lagrange interpolating polynomial at a given point.
- Parameters:
n (int) – Number of data points.
x (float) – The value at which to evaluate the polynomial.
points (list[list[float]]) – List of [xi, yi] data points.
- Example:
>>> points = [[1, 2], [2, 3], [4, 7]] >>> lagrange_interpolation(3, 2.5, points)
numerical_methods.interpolation.newton_interpolation module¶
- numerical_methods.interpolation.newton_interpolation.newton_interpolation(n: int, x: float, points: list[list[float]]) list[list[float]][source]¶
Evaluate the Newton interpolating polynomial at a given point using divided differences.
- Parameters:
n (int) – Number of data points.
x (float) – The value at which to evaluate the polynomial.
points (list[list[float]]) – List of [xi, yi] data points.
- Returns:
The divided difference table.
- Return type:
list[list[float]]
- Example:
>>> points = [[1, 2], [2, 3], [4, 7]] >>> newton_interpolation(3, 2.5, points)