Explain numerical stability and floating-point precision issues in MATLAB

Numerical stability in MATLAB refers to how algorithms handle floating-point errors and maintain accuracy under finite precision arithmetic.

MATLAB uses IEEE 754 double-precision floating-point arithmetic by default. While this provides high precision, it is still limited and introduces rounding errors.

Numerical instability occurs when small input errors produce large output deviations.

Key concepts:

Numbers are stored approximately, not exactly.

Repeated operations can accumulate small errors.

Subtracting nearly equal numbers leads to significant precision loss.

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