Maple worksheets on floating-point arithmetic and errors
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.
Maple's floating-point arithmetic - float.mws
- Floating-point numbers and the precision of computer arithmetic.
- Rounding and significant figures.
- Errors caused by rounding.
- Exact versus floating point arithmetic.
- Maple's hardware and software floating point arithmetic.
- The machine epsilon.
- A unit in the last place .. 1 ulp
Errors in computer floating point arithmetic - errors.mws
- Absolute and relative error.
- Rounding errors.
- Absolute and relative errors in relation to ulp's and the machine epsilon.
- The accumulation of rounding errors.
- Reducing rounding errors in a sum of positive terms.
Graphical illustration of the accumulation of rounding errors - errors2.mws
- An example to illustrate the accumulation of rounding errors graphically.
- Another example to illustrate the accumulation of rounding errors.
Subtraction round-off errors - errors3.mws
- Subtraction round-off error.
- Avoiding subtraction round-off errors.
- A family of integrals whose evaluation involves subtraction errors.
- Upward and downward recursion.
- Subtraction round-off error in the evaluation of ln(1-x)/x when x is near 0.
- Subtraction round-off error in the evaluation of (1-cos x)/x^2 when x is near 0.
Taylor series - taylor.mws
- Finding Taylor series and Taylor polynomials with Maple.
- Using Taylor polynomials to approximate functions.
Taylor series approximations for the exponential function - expsrs.mws
- Graphing partial sums of a Taylor series.
- Truncation error in computing partial sums.
- Writing a Maple procedure to evaluate the exponential function using partial sums of a Taylor series.
USING HARDWARE FLOATING POINT ARITHMETIC
Top of page