Maple worksheets on floating-point arithmetic and errors |

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.

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.

EVALUATION OF

USING HARDWARE FLOATING POINT ARITHMETIC