interpolation_divided_difference

interpolation_divided_difference, considers the use of Newton's divided difference methods for interpolation.

The notes:

• interpolation_divided_difference.pdf
• interpolation_divided_difference.tex

Scripts and functions:

• chebyspace.m, x=chebyspace(a,b,n) returns n points in [a,b] using Chebyshev spacing.
• data_to_difference_table.m, computes the full dxd difference table associated with a set of data.
• data_to_newton.m, computes the Newton representation of an interpolant to data.
• data_to_newton_test.m
• humps_newton_chebyspace.m, uses divided differences and chebyshev spacing to compute and plot the polynomial interpolant to the humps() function.
• humps_newton_linspace.m, uses divided differences and equal spacing to compute and plot the polynomial interpolant to the humps() function.
• newton_append.m, [c2,z2]=newton_append(c1,z1,x,y) updates an interpolating newton polynomial created by divided differences, by adding the new data point (x,y).
• newton_append_test.m
• newton_print.m, prints the Newton representation of a polynomial.
• newton_print_test.m
• newton_to_data.m, recovers the data that was used to create a Newton polynomial.
• newton_to_power.m, c2=newton_to_power(c1,z1) computes the power form coefficients of a polynomial that is in newton form.
• newton_to_power_test.m
• newton_value.m, value=newton_value(c,z,x) evaluates a Newton polynomial at the point x.
• newton_value_test.m
• poly_print.m, prints a polynomial.
• roots_to_newton.m, converts a list of roots to a Newton polynomial.
• roots_to_newton_test.m
• vec2_print.m, prints a pair of vectors.
• vector_print.m, prints a vector.
• vector_print_test.m

Images:

• divided_difference_table.png, a picture of the calculation of a divided difference table from data.
• humps_newton_chebyspace.png, a plot of the polynomial interpolant to humps, created by divided differences with chebyshev spacing.
• humps_newton_linspace.png, a plot of the polynomial interpolant to humps, created by divided differences with equal spacing.
• newton_value_test.png, a plot of a Newton interpolant to the tangent function.