Chapter 4
Numerical Errors and Uncertainty in Computation
Computers use finite precision, and numerical results must be interpreted with that limitation in mind. This chapter introduces number representation, rounding, cancellation, overflow, underflow, and truncation error. It discusses error propagation, numerical stability, conditioning, meaningful digits, and practical accuracy checks. It also distinguishes numerical error from uncertainty in input data, implementation mistakes, and limitations of the physical model.
In this chapter
- 4.1 Finite precision: how computers represent numbers
- 4.2 Sources of numerical error
- 4.3 Assessing numerical accuracy
- 4.4 Modeling and simulation errors
Companion resources
Codes
Floating-point precision, cancellation, and summation-order experiments, each included in one short program in MATLAB, Python, C++, and Fortran.
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Explanations of the numerical experiments, expected results, practical accuracy checks, and documentation for further reading.
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