Bottom SciencePython Programming
Basics
Numerical Methods
- Bisection Method
- Secant Method
- Regular Falsi (False Position) Method
- Newton Raphson Method
- Gauss Elimination Method
- Gauss Jordan Method
- Gauss-Seidel Method
- Lagrange Interpolation Method
- Newton Divided Difference Interpolation
- Newton Forward Difference Interpolation
- Newton Backward Difference Interpolation
- Trapezoidal Rule
- Simpson 1/3rd Rule
- Simpson 3/8 Rule
- Euler’s Method
- Euler’s Modified Method
- Runge-Kutta 2nd Order Method
- Runge-Kutta 4th Order Method
- Cubic Spline Method
- Bilinear Interpolation Method
- Milne’s Method
- More topics coming soon…
Advance Numerical Methods
Lagrange interpolation is a method of constructing a polynomial that passes through a given set of points.
This can be useful for curve fitting, data approximation, and other applications.
Lagrange Interpolation method in Python:
import numpy as np
def lagrange(x, y, t):
"""
Find the Lagrange polynomial through the points (x, y) and return its value at t.
"""
# Lagrange Interpolation Method [By Bottom Science]
# Check that the input arrays have the same length
if len(x) != len(y):
raise ValueError("The arrays x and y must have the same length.")
# Initialize the polynomial
p = 0
# Loop over the points
for i in range(len(x)):
# Get the current point
xi, yi = x[i], y[i]
# Initialize the term
term = yi
# Loop over the other points
for j in range(len(x)):
# Skip the current point
if i == j:
continue
# Multiply the term by the appropriate factor
term *= (t - x[j]) / (xi - x[j])
# Add the term to the polynomial
p += term
return p
#YOUR DATA POINTS
x = [0, 1, 2]
y = [0, 1, 4]
t = 0.5
p = lagrange(x, y, t)
print(p)
# OUTPUT - 0.25
