[2022 Fall] Assignment7-4¶

Course: AP3021

Q7-4¶

Repeat Q18.6 using Lagrange polynomials of order 1 to 3. (Python) (繪圖、值) Interpret your results in word or print in code¶

In [1]:

def NewtInt(x, y, n, x_miss):

    fdd = np.zeros((n, n))
    fdd[0:n, 0] = y[0:n]

    for j in range(1, n, 1):
        for i in range(0, n-j, 1):
            fdd[i, j] = (fdd[i + 1, j-1] - fdd[i, j - 1]) / (x[i + j] - x[i])

    y_interp = y[0]
    xterm = 1.0

    for order in range(1, n):
        xterm = xterm * (x_miss - x[order - 1])
        y_interp = y_interp + fdd[0, order] * xterm

    return y_interp

def NewtInt(x, y, n, x_miss): fdd = np.zeros((n, n)) fdd[0:n, 0] = y[0:n] for j in range(1, n, 1): for i in range(0, n-j, 1): fdd[i, j] = (fdd[i + 1, j-1] - fdd[i, j - 1]) / (x[i + j] - x[i]) y_interp = y[0] xterm = 1.0 for order in range(1, n): xterm = xterm * (x_miss - x[order - 1]) y_interp = y_interp + fdd[0, order] * xterm return y_interp

In [2]:

import numpy as np

x = [1, 2,  3,  5,   7,   8]
y = [3, 6, 19, 99, 291, 444]
n = 3
x_miss = 4

ans_New = NewtInt(x, y, n, x_miss)

print("Newton's interpolating polynomials f(4) =", ans_New)

import numpy as np x = [1, 2, 3, 5, 7, 8] y = [3, 6, 19, 99, 291, 444] n = 3 x_miss = 4 ans_New = NewtInt(x, y, n, x_miss) print("Newton's interpolating polynomials f(4) =", ans_New)

Newton's interpolating polynomials f(4) = 42.0

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Last update: 2024-04-27