Underflow is a form of rounding error that occurs when a number near zero is rounded to zero.

Underflow

Overflow is a form of rounding error that occurs when a large number is rounded to ∞ or -∞.

Overflow

This function is used to predict the probabilities of values in a multinoulli distribution. This function must be stabilized against underflow and overflow.

Softmax Function

Conditioning is used to describe the rate of change of a function as the input changes.
- The $\textbf{conditioning number}$ is used to describe how rapidly the function changes

Conditioning

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- Computation of transforms
- Computations in finite fields
- Computations on matrices
- Computations on polynomials
- Number-theoretic computations
- Interpolation
- Numerical differentiation
- Interval arithmetic
- Arbitrary-precision arithmetic
- Automatic differentiation
- Mesh generation
- Discretization

Numerical Analysis

Computations in finitie fields

Finding the minimum or maximum value of a function, $f(x)$, over a set of inputs, $\mathbb{S}$.  Points in $\mathbb{S}$ are called feasible points.

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