Variance Calculations: Difference between revisions
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[[File:Variance Calculations - Space.png|1000px]] | [[File:Variance Calculations - Space.png|1000px]] | ||
== Space | == Time-Space Tradeoff == | ||
[[File:Variance Calculations - Pareto Frontier.png|1000px]] | [[File:Variance Calculations - Pareto Frontier.png|1000px]] | ||
Revision as of 14:45, 15 February 2023
Description
Given a set of n (real/integer) numbers, compute the variance (sample or population). Of interest is streaming algorithms and numerical stability.
Parameters
n: number of values
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Naïve algorithm | 1940 | $O(n)$ | $O({1})$ auxiliary | Exact | Deterministic | |
| Two-pass algorithm | 1940 | $O(n)$ | $O({1})$ auxiliary | Exact | Deterministic | |
| Welford's Online algorithm | 1962 | $O(n)$ | $O({1})$ auxiliary | Exact | Deterministic | Time |
| Weighted incremental algorithm | 1979 | $O(n)$ | $O({1})$ auxiliary | Exact | Deterministic | Time |
| Chan's algorithm Parallel Implementation | 1979 | $O(log n)$ | $O({1})$ per processor | Exact | Parallel | Time |
Time Complexity Graph
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Space Complexity Graph
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Time-Space Tradeoff
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