cmlabs.interpolate.test_lagrange_compare_with_newton

cmlabs.interpolate.test_lagrange_compare_with_newton(degree)[source]

Compare Lagrange and Newton interpolation.

\[\begin{split}\begin{gather} L_n(x) = \sum_{i=0}^{n} l_i(x) f(x_i)\\ \\ L_n(x) = \sum_{i=0}^{n} f(x_0, x_1, \ldots, x_i) \omega_i(x) \end{gather}\end{split}\]

Results

>>> # Test 5: Compare Lagrange And Newton Interpolation Degree 1
>>> # - X:  [0.5   0.556 0.611 ... 0.889 0.944 1.   ]
>>> # - Y:  [0.102 0.148 0.194 ... 0.428 0.475 0.523]
>>> # - x* =  0.77
>>> # Nearest points: [0.722 0.778]
>>> # Nearest f(x) values: [0.287 0.334]
>>> lagrange([0.722 0.778], [0.287 0.334], 0.77)
>>> # 0.327530850170338
>>> newton([0.722 0.778], 0.77, yvals=[0.287 0.334])
>>> # 0.327530850170338

>>> # Test 6: Compare Lagrange And Newton Interpolation Degree 2
>>> # - X:  [0.5   0.556 0.611 ... 0.889 0.944 1.   ]
>>> # - Y:  [0.102 0.148 0.194 ... 0.428 0.475 0.523]
>>> # - x* =  0.77
>>> # Nearest points: [0.722 0.778 0.833]
>>> # Nearest f(x) values: [0.287 0.334 0.381]
>>> lagrange([0.722 0.778 0.833], [0.287 0.334 0.381], 0.77)
>>> # 0.3275203902670937
>>> newton([0.722 0.778 0.833], 0.77, yvals=[0.287 0.334 0.381])
>>> # 0.3275203902670936