Maple worksheets on polynomial interpolation
Numerical methods topics:
- Introduction - errors
- 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 map and zip.
- 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 - interpoly
- interpoly: 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
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