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 refers to how rapidly the output of a function changes in response to small changes in its input. This sensitivity is quantified by the $$\textbf{condition number}$$, which measures the rate of change of the function as the input varies.

Function 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

Constrained optimization is the mathematical process of finding the minimum or maximum value of an objective function, $$f(x)$$, over a restricted set of inputs, $$\mathbb{S}$$. The points in $$\mathbb{S}$$ that satisfy the problem's constraints are called feasible points.

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