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# Freivalds' algorithm

Freivalds' algorithm (named after Rūsiņš Mārtiņš Freivalds) is a probabilistic randomized algorithm used to verify matrix multiplication. [1]

## Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

## Bayes' theorem

In probability theory and statistics, Bayes’ theorem (alternatively Bayes’ law or Bayes' rule, also written as Bayes’s theorem) describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

## Big O notation

Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.

In linear algebra, the Coppersmith–Winograd algorithm, named after Don Coppersmith and Shmuel Winograd, was the asymptotically fastest known matrix multiplication algorithm until 2010.

## Deterministic algorithm

In computer science, a deterministic algorithm is an algorithm which, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states.

## Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

## Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

## Matrix multiplication

In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.

## Monte Carlo algorithm

In computing, a Monte Carlo algorithm is a randomized algorithm whose output may be incorrect with a certain (typically small) probability.

## Probability

Probability is the measure of the likelihood that an event will occur.

## Randomization

Randomization is the process of making something random; in various contexts this involves, for example.

## Randomized algorithm

A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic.

## Randomness

Randomness is the lack of pattern or predictability in events.

## Rūsiņš Mārtiņš Freivalds

Rūsiņš Mārtiņš Freivalds (10 November 1942 &ndash; 4 January 2016) was a Latvian computer scientist and mathematician.

## Schwartz–Zippel lemma

In mathematics, the Schwartz–Zippel lemma (also called the DeMillo-Lipton-Schwartz–Zippel lemma) is a tool commonly used in probabilistic polynomial identity testing, i.e. in the problem of determining whether a given multivariate polynomial is the 0-polynomial (or identically equal to 0).

## With high probability

In mathematics, an event that occurs with high probability (often shortened to w.h.p. or WHP) is one whose probability depends on a certain number n and goes to 1 as n goes to infinity, i.e. it can be made as close as desired to 1 by making n big enough.

## References

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