Maple worksheets on polynomial interpolation |

Numerical methods topics:

- Introduction - errors
- Root-finding
- Interpolation
- Numerical integration
- 1st order differential equations
- 2nd order differential equations
- Linear systems
- Finite difference methods
- The Duffing equation
- Approximation of functions
- The numerical evaluation of mathematical functions
- Special inverse functions
- The derivation of Runge-Kutta schemes
- Interpolation for Runge-Kutta schemes

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

Introduction- interp.mws

- An introduction to polynomial interpolation: finding the coefficients of an interpolating polynomial by solving a system of equations.

The Lagrange form of the interpolating polynomial- lagrange.mws

- Construction of the Lagrange interpolating polynomial.
- A procedure for constructing the Lagrange interpolating polynomial:
lagrange_interp

Working with interpolating polynomials- interp2.mws

- Evaluation of polynomials in nested form:
convert( . . , horner).- Constructing functions from expressions using
unapply.- The Maple procedures
mapandzip.- Constructing interpolating polynomials with
interp.

The accuracy of an interpolating polynomial- rungexamp.mws

- Investigations involving the Runge example.

Interpolation with unevenly spaced interpolation points- chebyshev.mws

- Description of Chebyshev polynomials.
- Constructing interpolating polynomials with spacing given by the zeros of Chebyshev polynomials.

The Newton interpolation formula- divdiff.mws

- Divided differences.
- The Newton divided differences interpolation formula.
- A procedure for constructing a Newton interpolating polynomial:
newton_interp

Using interpolating polynomials to approximate functions- interpoly.mws

- A procedure constructing an interpolating polynomial approximation -
interpolyinterpoly: examples with evenly spaced nodes- Using an interpolating polynomial to emulate a finite Chebyshev series
interpoly: general examples

Inverse interpolation and root-finding- invinterp.mws

- Constructing an interpolating polynomial to provide a local inverse for a function, and using it to estimate a zero of the function.
- An iterative root-finding scheme which uses inverse interpolation.
- A procedure for graphing successive steps of the inverse interpolation method:
interproot_step- A procedure implementing a root-finding method which uses inverse interpolation:
interproot.

Root-finding for functions of a complex variable- zeta.mws

- Iterative methods of root-finding for functions of a complex variable.
- Finding zeros of the Riemann zeta function.

Function approximation and interpolation procedures- fcnapprx.zip