polynomial_operations

polynomial_operations, considers the representation, evaluation, arithmetic operations, differentiation, and anti-differentiation of polynomial functions.

The notes:

• polynomial_operations.pdf
• polynomial_operations.tex

Scripts:

• evaluation_compare.m, evaluation_compare(x) compares double and single precision versions of four methods of evaluating a particular polynomial.
• factor_to_poly.m, converts a polynomial from factor form to power form.
• factor_value.m, evaluates a polynomial in factor form.
• factor_value_single.m, evaluates a polynomial in factor form using single precision.
• newton_value.m, evaluates a polynomial in Newton form.
• newton_value_test.m
• poly_add.m, adds two polynomials.
• poly_antideriv.m, computes the antiderivative of a polynomial.
• poly_deriv.m, computes the derivative of a polynomial.
• poly_divide.m, divides one polynomial by another.
• poly_divide_test.m
• poly_multiply.m, multiplies two polynomials.
• poly_norm.m, computes the L2 norm of a polynomial.
• poly_power.m, computes a power of a polynomial.
• poly_print.m, prints a polynomial.
• poly_print_test.m
• poly_square.m, squares a polynomial.
• poly_to_factor.m, converts a polynomial from power form to factor form, using MATLAB's roots() function.
• poly_value_nested.m, uses nested multiplication to evaluate a polynomial.
• poly_value_nested_single.m, uses nested multiplication to evaluate a polynomial, in single precision.
• poly_value_termwise.m, uses termwise multiplication to evaluate a polynomial.
• poly_value_termwise_single.m, uses termwise multiplication to evaluate a polynomial, in single precision.
• r8poly_print.m, prints a polynomial.
• r8poly_print_test.m

Text:

• evaluation_compare.txt, the output from evaluation_compare(314.15).

Images:

• newton_value_test.png, compares the tangent function and a Newton polynomial approximation.
• polynomial_plot.png, a closeup of three plots of the same polynomial using different representations.