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Recursive algorithm for matrix multiplication
In linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm for matrix multiplication. It is faster than the standard matrix
Strassen_algorithm
Multiplication algorithm
Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers, published by Arnold Schönhage and Volker Strassen in 1971
Schönhage–Strassen_algorithm
Algorithm to multiply two numbers
factor also grows, making it impractical. In 1968, the Schönhage–Strassen algorithm, which makes use of a Fourier transform over a modulus, was discovered
Multiplication_algorithm
German mathematician and algorithms researcher (b.1936)
influential contributions to the design and analysis of efficient algorithms." Strassen was born on April 29, 1936, in Düsseldorf-Gerresheim. After studying
Volker_Strassen
Probabilistic primality test
The Solovay–Strassen primality test, developed by Robert M. Solovay and Volker Strassen in 1977, is a probabilistic primality test to determine if a number
Solovay–Strassen primality test
Solovay–Strassen_primality_test
Algorithm to multiply matrices
the time required to multiply matrices have been known since the Strassen's algorithm in the 1960s, but the optimal time (that is, the computational complexity
Matrix multiplication algorithm
Matrix_multiplication_algorithm
Algorithm for integer multiplication
"grade school" algorithm. The Toom–Cook algorithm (1963) is a faster generalization of Karatsuba's method, and the Schönhage–Strassen algorithm (1971) is even
Karatsuba_algorithm
Algorithmic runtime requirements for matrix multiplication
straightforward "schoolbook algorithm". The first to be discovered was Strassen's algorithm, devised by Volker Strassen in 1969 and often referred to
Computational complexity of matrix multiplication
Computational_complexity_of_matrix_multiplication
Type of randomized algorithm
times. Consider again the Solovay–Strassen algorithm which is 1⁄2-correct false-biased. One may run this algorithm multiple times returning a false answer
Monte_Carlo_algorithm
Coppersmith–Winograd algorithm: square matrix multiplication Freivalds' algorithm: a randomized algorithm used to verify matrix multiplication Strassen algorithm: faster
List_of_algorithms
Method for division with remainder
efficient multiplication algorithm such as the Karatsuba algorithm, Toom–Cook multiplication or the Schönhage–Strassen algorithm. The result is that the
Division_algorithm
Artificial intelligence system for discovering matrix multiplication algorithms
The standard algorithm for multiplying two square matrices has cubic time complexity, while faster algorithms such as the Strassen algorithm reduce the
AlphaTensor
Discrete Fourier transform algorithm
Odlyzko–Schönhage algorithm applies the FFT to finite Dirichlet series Schönhage–Strassen algorithm – asymptotically fast multiplication algorithm for large integers
Fast_Fourier_transform
Algorithmic runtime requirements for common math procedures
The following tables list the computational complexity of various algorithms for common mathematical operations. Here, complexity refers to the time complexity
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Overview of and topical guide to algorithms
Karatsuba algorithm Schönhage–Strassen algorithm Gaussian elimination LU decomposition QR decomposition Singular value decomposition Eigenvalue algorithm Strassen
Outline_of_algorithms
German mathematician and computer scientist
in Tübingen and Konstanz. Together with Volker Strassen, he developed the Schönhage–Strassen algorithm for the multiplication of large numbers that has
Arnold_Schönhage
Topics referred to by the same term
Strassen may refer to: Volker Strassen, mathematician Strassen algorithm Strassen, Luxembourg, town and commune Strassen, Tyrol, town in the district of
Strassen
Algorithm for multiplying large numbers
intermediate-size multiplications, before the asymptotically faster Schönhage–Strassen algorithm (with complexity Θ ( n log n log log n ) {\displaystyle \Theta
Toom–Cook_multiplication
Estimate of time taken for running an algorithm
calculation, O ( n log n ) {\displaystyle O(n\log n)} Schönhage–Strassen algorithm for multiplication, O ( n log n log log n ) {\displaystyle O(n\log
Time_complexity
Classification of algorithm
operations) was the Strassen algorithm: a recursive algorithm that takes O ( n 2.807 ) {\displaystyle O(n^{2.807})} operations. This algorithm is not galactic
Galactic_algorithm
Algorithms which recursively solve subproblems
efficient algorithms. It was the key, for example, to Karatsuba's fast multiplication method, the quicksort and mergesort algorithms, the Strassen algorithm for
Divide-and-conquer_algorithm
Probabilistic primality test
test: an algorithm which determines whether a given number is likely to be prime, similar to the Fermat primality test and the Solovay–Strassen primality
Miller–Rabin_primality_test
AI-powered evolutionary coding agent
Recursive self-improvement Strassen algorithm "AlphaEvolve: A Gemini-powered coding agent for designing advanced algorithms". Google DeepMind. 2025-05-14
AlphaEvolve
Calculations where numbers' precision is only limited by computer memory
{\displaystyle \mathbb {Z} } . Fürer's algorithm Karatsuba algorithm Mixed-precision arithmetic Schönhage–Strassen algorithm Toom–Cook multiplication Little
Arbitrary-precision arithmetic
Arbitrary-precision_arithmetic
Decomposition of a number into a product
efficient non-quantum integer factorization algorithm is known. However, it has not been proven that such an algorithm does not exist. The presumed difficulty
Integer_factorization
Algorithm for computing greatest common divisors
series, showing that it is also O(h2). Modern algorithmic techniques based on the Schönhage–Strassen algorithm for fast integer multiplication can be used
Euclidean_algorithm
Mathematical operation in linear algebra
not optimal, as shown in 1969 by Volker Strassen, who provided an algorithm, now called Strassen's algorithm, with a complexity of O ( n log 2 7 ) ≈
Matrix_multiplication
Algorithm in computational number theory
Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm
Algorithm for computing the greatest common divisor
The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor
Binary_GCD_algorithm
algorithm for indefinite integration developed by Robert Henry Risch 1969 – Strassen algorithm for matrix multiplication developed by Volker Strassen
Timeline_of_algorithms
Algorithmic technique
multiplication techniques such as Toom–Cook multiplication and the Schönhage–Strassen algorithm must be used; with ordinary O(n2) multiplication, binary splitting
Binary_splitting
Computer system for solving algebra problems
contains asymptotically fast algorithms for all fundamental integer and polynomial operations, such as the Schönhage–Strassen algorithm for fast multiplication
Magma (computer algebra system)
Magma_(computer_algebra_system)
Quantum algorithm for integer factorization
Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor
Shor's_algorithm
Algorithm that employs a degree of randomness as part of its logic or procedure
randomized algorithm for efficiently computing the roots of a polynomial over a finite field. In 1977, Robert M. Solovay and Volker Strassen discovered
Randomized_algorithm
Method for computing the relation of two integers with their greatest common divisor
and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common
Extended_Euclidean_algorithm
Arithmetical operation
Multiplication algorithm Karatsuba algorithm, for large numbers Toom–Cook multiplication, for very large numbers Schönhage–Strassen algorithm, for huge numbers
Multiplication
Integral expressing the amount of overlap of one function as it is shifted over another
discarding portions of the output. Other fast convolution algorithms, such as the Schönhage–Strassen algorithm or the Mersenne transform, use fast Fourier transforms
Convolution
AI research laboratory
found an algorithm requiring only 47 distinct multiplications; the previous optimum, known since 1969, was the more general Strassen algorithm, using 49
Google_DeepMind
Ancient algorithm for generating prime numbers
In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking
Sieve_of_Eratosthenes
Test if a Mersenne number is prime
complexity is O(p3). A more efficient multiplication algorithm is the Schönhage–Strassen algorithm, which is based on the Fast Fourier transform. It only
Lucas–Lehmer_primality_test
Integer factorization algorithm
Pollard's rho algorithm is an algorithm for integer factorization. It was invented by John Pollard in 1975. It uses only a small amount of space, and
Pollard's_rho_algorithm
Branch of elementary mathematics
integers, such as the Karatsuba algorithm, the Schönhage–Strassen algorithm, and the Toom–Cook algorithm. A common technique used for division is called long
Arithmetic
Product of numbers from 1 to n
O ( n log n ) {\displaystyle b=O(n\log n)} bits. The Schönhage–Strassen algorithm can produce a b {\displaystyle b} -bit product in time O ( b log
Factorial
Mapping function that preserves data point locality
and, in fact, was used in an optimized index, the S2-geometry. The Strassen algorithm for matrix multiplication is based on splitting the matrices in four
Z-order_curve
Type of Diophantine equation
using the continued fraction method, with the aid of the Schönhage–Strassen algorithm for fast integer multiplication, is within a logarithmic factor of
Pell's_equation
Exponent of a power of two
divide and conquer algorithms, such as the Karatsuba algorithm for multiplying n-bit numbers in time O(nlog2 3), and the Strassen algorithm for multiplying
Binary_logarithm
rule Gaussian elimination Gauss–Jordan elimination Overcompleteness Strassen algorithm Matrix Matrix addition Matrix multiplication Basis transformation
Outline_of_linear_algebra
Generalisation of Fourier transform to any ring
as the Fermat Number Transform (m = 2k+1), used by the Schönhage–Strassen algorithm, or Mersenne Number Transform (m = 2k − 1) use a composite modulus
Discrete Fourier transform over a ring
Discrete_Fourier_transform_over_a_ring
Standard model in theoretical computer science
polynomials, some clever circuits (alternatively algorithms) were found. A well-known example is Strassen's algorithm for matrix product. The straightforward way
Arithmetic_circuit_complexity
Array of numbers
the product, n multiplications are necessary. The Strassen algorithm outperforms this "naive" algorithm; it needs only n2.807 multiplications. Theoretically
Matrix_(mathematics)
Java math library
and optimization. It implements a parallel version of the adaptive strassen's algorithm for fast matrix multiplication. SuanShu has been quoted and used
SuanShu_numerical_library
Algorithm for determining whether a number is prime
subsequent discovery of the Solovay–Strassen and Miller–Rabin algorithms put PRIMES in coRP. In 1992, the Adleman–Huang algorithm reduced the complexity to
Primality_test
Mathematical procedure
a_{1}x_{1}+a_{2}x_{2}+\cdots +a_{n}x_{n}=0.\,} An integer relation algorithm is an algorithm for finding integer relations. Specifically, given a set of real
Integer_relation_algorithm
zero matrix Algorithms for matrix multiplication: Strassen algorithm Coppersmith–Winograd algorithm Cannon's algorithm — a distributed algorithm, especially
List of numerical analysis topics
List_of_numerical_analysis_topics
Mathematical algorithm
Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, analogous to Pollard's
Pollard's rho algorithm for logarithms
Pollard's_rho_algorithm_for_logarithms
Algorithm for computing logarithms
theory, the Pohlig–Hellman algorithm, sometimes credited as the Silver–Pohlig–Hellman algorithm, is a special-purpose algorithm for computing discrete logarithms
Pohlig–Hellman_algorithm
algorithm (for polynomial factorization) Lindsey–Fox algorithm Remez algorithm (to find best approximating polynomials) Schönhage–Strassen algorithm Polynomial
List_of_polynomial_topics
Algorithm used in modular arithmetic
The Tonelli–Shanks algorithm (referred to by Shanks as the RESSOL algorithm) is used in modular arithmetic to solve for r in a congruence of the form r2
Tonelli–Shanks_algorithm
for which the multiplication algorithm of Harvey and van der Hoeven (2019) is faster than the Schönhage–Strassen algorithm. Cosmology: The estimated number
Orders_of_magnitude_(numbers)
Measure of a systems floating point architecture
taken as the operation count, with independence of the algorithm used. Use of the Strassen algorithm is not allowed because it distorts the real execution
LINPACK_benchmarks
Routines for performing common linear algebra operations
matrix multiplications and two real matrix additions", an algorithm similar to Strassen algorithm first described by Peter Ungar. Accelerate Apple's framework
Basic Linear Algebra Subprograms
Basic_Linear_Algebra_Subprograms
Special-purpose algorithm for factoring integers
Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974. It is a special-purpose algorithm, meaning
Pollard's_p_−_1_algorithm
Vector satisfying some of the criteria of an eigenvector
rule Gaussian elimination Gauss–Jordan elimination Overcompleteness Strassen algorithm Matrices Matrix Matrix addition Matrix multiplication Basis transformation
Generalized_eigenvector
Algorithm for integer factorization
elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer factorization, which employs elliptic curves. For general-purpose
Lenstra elliptic-curve factorization
Lenstra_elliptic-curve_factorization
Software testing technique that tests programs with random inputs
simple algorithm in a much more complex way for better performance. For example, to test an implementation of the Schönhage–Strassen algorithm, the standard
Random_testing
Algorithm checking for prime numbers
test and the cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal, Neeraj Kayal, and Nitin Saxena
AKS_primality_test
Measure of algorithm performance for large inputs
multiplication has a weak form of speed-up among a restricted class of algorithms (Strassen-type bilinear identities with lambda-computation). Element uniqueness
Asymptotically optimal algorithm
Asymptotically_optimal_algorithm
Fast greatest common divisor algorithm
GCD algorithm, named after D. H. Lehmer, is a fast GCD algorithm for multiple-precision arithmetic, which improves on the simpler Euclidean algorithm by
Lehmer's_GCD_algorithm
Algorithm in computational number theory
kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced
Pollard's_kangaroo_algorithm
Matrix defined using smaller matrices called blocks
vector space) Strassen algorithm (algorithm for matrix multiplication that is faster than the conventional matrix multiplication algorithm) Eves, Howard
Block_matrix
Problem of inverting exponentiation in groups
Index calculus algorithm Number field sieve Pohlig–Hellman algorithm Pollard's rho algorithm for logarithms Pollard's kangaroo algorithm (aka Pollard's
Discrete_logarithm
Integers that satisfy a specific condition
probable primes (P = 1/4, Miller–Rabin algorithm), or Euler probable primes (P = 1/2, Solovay–Strassen algorithm). Even when a deterministic primality
Probable_prime
Factorization algorithm
the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100. Heuristically, its complexity
General_number_field_sieve
Largest integer that divides given integers
|a|. This case is important as the terminating step of the Euclidean algorithm. The above definition is unsuitable for defining gcd(0, 0), since there
Greatest_common_divisor
In computational number theory, Cipolla's algorithm is a technique for solving a congruence of the form x 2 ≡ n ( mod p ) , {\displaystyle x^{2}\equiv
Cipolla's_algorithm
Integer factorization algorithm
The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second-fastest method known (after the general number field
Quadratic_sieve
Public university in Bonn, Germany
Hirzebruch–Riemann–Roch theorem, Lipschitz continuity, the Petri net, the Schönhage–Strassen algorithm, Faltings' theorem and the Toeplitz matrix are all named after University
University_of_Bonn
Integer factorization algorithm
theory, Williams's p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by
Williams's_p_+_1_algorithm
System of rapid mental calculation
This article presents some methods devised by Trachtenberg. Some of the algorithms Trachtenberg developed are for general multiplication, division and addition
Trachtenberg_system
Probabilistic algorithm for computing discrete logarithms
In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete
Index_calculus_algorithm
Exponentation in modular arithmetic
multiplicative inverse d of b modulo m (for instance by using extended Euclidean algorithm). More precisely: c = be mod m = d−e mod m, where e < 0 and b ⋅ d ≡ 1
Modular_exponentiation
Algorithm in number theory
(also Dixon's random squares method or Dixon's algorithm) is a general-purpose integer factorization algorithm; it is the prototypical factor base method
Dixon's_factorization_method
Integer factorization algorithm
x-y} will give a non-trivial factor of N {\displaystyle N} . A practical algorithm for finding pairs ( x , y ) {\displaystyle (x,y)} which satisfy x 2 ≡
Shanks's square forms factorization
Shanks's_square_forms_factorization
Special-purpose integer factorization algorithm
number field sieve (SNFS) is a special-purpose integer factorization algorithm. The general number field sieve (GNFS) was derived from it. The special
Special_number_field_sieve
Multiplication algorithm
ancient Egypt the concept of base 2 did not exist, the algorithm is essentially the same algorithm as long multiplication after the multiplier and multiplicand
Ancient Egyptian multiplication
Ancient_Egyptian_multiplication
Soviet American mathematician
{\displaystyle O(n^{2.795})} . This was the first improvement over the Strassen algorithm after nearly a decade, and kicked off a long line of improvements
Victor_Pan
Efficient algorithm to count points on elliptic curves
Schoof's algorithm is an efficient algorithm to count points on elliptic curves over finite fields. The algorithm has applications in elliptic curve cryptography
Schoof's_algorithm
Number-theoretic algorithm
In computational number theory, Cornacchia's algorithm is an algorithm for solving the Diophantine equation x 2 + d y 2 = m {\displaystyle x^{2}+dy^{2}=m}
Cornacchia's_algorithm
sc. in 1974), of Beno Eckmann (Topology and Geometry) and Volker Strassen (Algorithmics), and in Warsaw of Andrzej Mostowski and Witek Marek, where he spent
Johann_Makowsky
Method in number theory
In number theory, Berlekamp's root finding algorithm, also called the Berlekamp–Rabin algorithm, is the probabilistic method of finding roots of polynomials
Berlekamp–Rabin_algorithm
Algorithm for generating prime numbers
Sundaram is a variant of the sieve of Eratosthenes, a simple deterministic algorithm for finding all the prime numbers up to a specified integer. It was discovered
Sieve_of_Sundaram
Greatest integer less than or equal to square root
y {\displaystyle y} and k {\displaystyle k} be non-negative integers. Algorithms that compute (the decimal representation of) y {\displaystyle {\sqrt {y}}}
Integer_square_root
Algorithms to generate prime numbers
In computational number theory, a variety of algorithms make it possible to generate prime numbers efficiently. These are used in various applications
Generation_of_primes
Algorithm for solving the discrete logarithm problem
branch of mathematics, the baby-step giant-step is a meet-in-the-middle algorithm for computing the discrete logarithm or order of an element in a finite
Baby-step_giant-step
Methods to test or prove primality
Goldwasser and Joe Kilian in 1986 and turned into an algorithm by A. O. L. Atkin in the same year. The algorithm was altered and improved by several collaborators
Elliptic_curve_primality
Algorithm for generating prime numbers
In mathematics, the sieve of Pritchard is an algorithm for finding all prime numbers up to a specified bound. Like the ancient sieve of Eratosthenes,
Sieve_of_Pritchard
Integer factorization algorithm
most laborious but easiest to understand of the integer factorization algorithms. The essential idea behind trial division tests to see if an integer n
Trial_division
Algorithm for determining whether a number is prime
Adleman–Pomerance–Rumely primality test is an algorithm for determining whether a number is prime. Unlike other, more efficient algorithms for this purpose, it avoids the
Adleman–Pomerance–Rumely primality test
Adleman–Pomerance–Rumely_primality_test
Algorithm for generating prime numbers
In mathematics, the sieve of Atkin is a modern algorithm for finding all prime numbers up to a specified integer. Compared with the ancient sieve of Eratosthenes
Sieve_of_Atkin
Integer factorization algorithm
In mathematics, the rational sieve is a general algorithm for factoring integers into prime factors. It is a special case of the general number field
Rational_sieve
STRASSEN ALGORITHM
STRASSEN ALGORITHM
Boy/Male
Hindu, Indian, Marathi
With an Army of Gods
Surname or Lastname
English
English : habitational name from any of the various places, for example in Hertfordshire, Kent, and Somerset, so named from Old English strǣt ‘paved highway’, ‘Roman road’ (Latin strata (via)). In the Middle Ages the word at first denoted a Roman road but later also came to denote the main street in a town or village, and so the surname may also have been a topographic name for someone who lived on a main street.Jewish : Americanized form of the Sephardic surname Chetrit, of uncertain origin.Americanized form of Ashkenazic Jewish Strasser and a number of other similar surnames.The Rev. Nicholas Street (1603–74) came from England to Taunton, MA, between 1630 and 1638, and later moved to New Haven, CT, where his descendant Augustus Russell Street, a leader in art education, was born in 1791 and went on to become one of the most important early benefactors of Yale College.
STRASSEN ALGORITHM
STRASSEN ALGORITHM
Boy/Male
Hindu
Male
Swedish
Swedish variant spelling of Scandinavian Henrik, HENRIC means "home-ruler."
Girl/Female
Hindu, Indian, Traditional
Determine to Achieve the Goal
Boy/Male
Arabic, Muslim
Sentence; Writing; Essay; Famous Poet; Blessing; Ibn-e-insha
Boy/Male
Tamil
Sarvaraidu | ஸரà¯à®µà®°à®¾à®ˆà®Ÿà¯à®‚
Ruler of entire universe
Boy/Male
Indian, Tamil
Always Happy
Boy/Male
Hindu
Young
Girl/Female
Tamil
Pakshalika | பகà¯à®·à®¾à®²à®¿à®•à®¾
On the right path
Girl/Female
French
Birthday; especially the birthday of Christ.
Girl/Female
Hindu, Indian, Marathi
Most Beautiful; Well Adorned
STRASSEN ALGORITHM
STRASSEN ALGORITHM
STRASSEN ALGORITHM
STRASSEN ALGORITHM
STRASSEN ALGORITHM
v. t.
See Straiten.
v. t.
To draw tighter; to straiten; to make more close in any manner.
v. t.
A variant of Straiten.
v. t.
To make strait; to make narrow; hence, to contract; to confine.
v. t.
To restrict; to distress or embarrass in respect of means or conditions of life; -- used chiefly in the past participle; -- as, a man straitened in his circumstances.
v. t.
To make too small or short; to limit or straiten; to put on short allowance; to scant; to contract; to shorten; as, to scrimp the pattern of a coat.
n.
A highly refractive vitreous composition, variously colored, used in making imitations of precious stones or gems. See Strass.
v. t.
To make tense, or tight; to tighten.
a.
To press together; to crowd; to straiten; to confine closely.
imp. & p. p.
of Straiten
n.
A brilliant glass, used in the manufacture of artificial paste gems, which consists essentially of a complex borosilicate of lead and potassium. Cf. Glass.
v.
To straiten; to distress; as, to be pressed with want or hunger.
n.
The art of calculating by nine figures and zero.
n.
Alt. of Algorithm
v. t.
To limit; to straiten; to treat illiberally; to stint; as, to scant one in provisions; to scant ourselves in the use of necessaries.
v. t.
Figuratively: To cramp; to straiten; to oppress; to starve; to distress; as, to be pinched for money.
p. pr. & vb. n.
of Straiten
n.
The art of calculating with any species of notation; as, the algorithms of fractions, proportions, surds, etc.