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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
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
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 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
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
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
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
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
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
Coppersmith–Winograd algorithm: square matrix multiplication Freivalds' algorithm: a randomized algorithm used to verify matrix multiplication Strassen algorithm: faster
List_of_algorithms
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
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
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
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
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
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
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
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
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
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
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
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
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
algorithm for indefinite integration developed by Robert Henry Risch 1969 – Strassen algorithm for matrix multiplication developed by Volker Strassen
Timeline_of_algorithms
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
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 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
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
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
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)
algorithm (for polynomial factorization) Lindsey–Fox algorithm Remez algorithm (to find best approximating polynomials) Schönhage–Strassen algorithm Polynomial
List_of_polynomial_topics
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
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 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
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
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
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
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
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)
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
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
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
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
Arithmetical operation
Multiplication algorithm Karatsuba algorithm, for large numbers Toom–Cook multiplication, for very large numbers Schönhage–Strassen algorithm, for huge numbers
Multiplication
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
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
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
rule Gaussian elimination Gauss–Jordan elimination Overcompleteness Strassen algorithm Matrix Matrix addition Matrix multiplication Basis transformation
Outline_of_linear_algebra
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
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
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
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)
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
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
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
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
Two raised to an integer power
the O(n log n) multiplication algorithm of Harvey and van der Hoeven (2019) is faster than the Schönhage–Strassen algorithm. 2265536 = ..
Power_of_two
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
Prize in foundations of computer science
April 2007 ACM SIGACT 2008 Knuth Prize Recognizes Strassen for Contributions to Efficient Algorithm Design, ACM, October 23, 2008 Linda Crane, David S
Knuth_Prize
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
Longest distance between two vertices
Marek; Gabow, Harold N.; Sankowski, Piotr (2012), "Algorithmic applications of Baur-Strassen's theorem: shortest cycles, diameter and matchings", 53rd
Diameter_(graph_theory)
Number divisible only by 1 and itself
Monte Carlo) algorithms, meaning that they have a small random chance of producing an incorrect answer. For instance the Solovay–Strassen primality test
Prime_number
converse is not necessarily true. Grantham's stated goal when developing the algorithm was to provide a test that primes would always pass and composites would
Quadratic_Frobenius_test
Israeli mathematician and computer scientist (1931–2026)
cryptography, and in 2003 Miller, Rabin, Robert M. Solovay, and Volker Strassen were given the Paris Kanellakis Award for their work on primality testing
Michael_O._Rabin
Algorithms for polynomial evaluation
polynomial that cannot be computed in time much smaller than its degree? Volker Strassen has shown that the polynomial P ( x ) = ∑ k = 0 n 2 2 k n 3 x k {\displaystyle
Polynomial_evaluation
Probabilistic primality test
extensions of the Fermat test, such as Baillie–PSW, Miller–Rabin, and Solovay–Strassen are more commonly used. In general, if n {\displaystyle n} is a composite
Fermat_primality_test
Award in theoretical computer science
the FM-index". awards.acm.org. Retrieved 2023-07-11. "Contributors to Algorithm Engineering Receive Kanellakis Award". awards.acm.org. Retrieved 2024-06-19
Paris_Kanellakis_Award
Formula for systems of linear equations
multiplication was proposed.. For example, for the Strassen's Multiplication Algorithm, this algorithm computes the solution in ( 7 / 15 ) n log 2 ( 7
Cramer's_rule
Free library for arbitrary precision arithmetic
kernel for speed-critical inner loops and implements advanced algorithms like Schönhage–Strassen multiplication, binary splitting for computing certain mathematical
Class_Library_for_Numbers
Methods used to exchange information
Lexikon der Kommunikationspolitik, 2011, S. 64 Charles Franz Zimpel, Straßen-Verbindung des Mittelländischen mit dem Todten Meere …, 1865, S. 3 Albert
Means_of_communication
Swiss mathematician and theoretical computer scientist
Trägerfunktional bilinearer Abbildungen under the supervision of Volker Strassen. Bürgisser was a postdoc at the University of Bonn from 1991 to 1993 and
Peter_Bürgisser
Integer that is a perfect square modulo some integer
composite the formula may or may not compute (a|p) correctly. The Solovay–Strassen primality test for whether a given number n is prime or composite picks
Quadratic_residue
Strachey – denotational semantics Volker Strassen – matrix multiplication, integer multiplication, Solovay–Strassen primality test Bjarne Stroustrup – C++
List_of_computer_scientists
American computer scientist
central topics in computer science, including graph isomorphism, parallel algorithms, computational geometry and scientific computing. His most recent focus
Gary Miller (computer scientist)
Gary_Miller_(computer_scientist)
Generalization of the Legendre symbol in number theory
n is "probably prime". This is the basis for the probabilistic Solovay–Strassen primality test and refinements such as the Baillie–PSW primality test and
Jacobi_symbol
Mathematical theorem
of the iterated logarithm for the absolute value of a brownian motion. Strassen (1964) studied the LIL from the point of view of invariance principles
Law_of_the_iterated_logarithm
Composite number that passes Fermat's probable primality test
analogues of Carmichael numbers. This leads to probabilistic algorithms such as the Solovay–Strassen primality test, the Baillie–PSW primality test, and the
Fermat_pseudoprime
Formula concerning prime numbers
comparing them can be used as a primality test, specifically the Solovay–Strassen primality test. Composite numbers for which the congruence holds for a
Euler's_criterion
Decomposition in multilinear algebra
generic rank of tensor spaces was initially studied in 1983 by Volker Strassen. As an illustration of the above concepts, it is known that both 2 and
Tensor_rank_decomposition
Optical character recognition technology
the observance of travel behavior". Universität Stuttgart Institut für Straßen und Verkehrswesen. Retrieved 2 July 2013. Friedrich, Markus; Jehlicka,
Automatic number-plate recognition
Automatic_number-plate_recognition
Argentinean-Swiss mathematician (born 1945)
to receive a PhD in mathematics in 1982 under the supervision of Volker Strassen. He performed his habilitation in 1986 at the J.W.von Goethe University
Joos_Ulrich_Heintz
Primality test for numbers of a certain form
but not conclusive, of primality. Refer to the probabilistic Solovay–Strassen primality test and the Miller-Rabin test. Inconclusive result: b = 1, in
Proth's_theorem
German word meaning "subhuman", used by the Nazis
Räteherrschaft. Als das losgelassene Untermenschentum mordend durch die Straßen zog, da versteckten sich Abgeordnete hinter einem Kamin im bayerischen
Untermensch
Swiss-Canadian civil engineer
Maintenance Management". VSS Mobilityplatform. Schweizerischer Verband der Strassen- und Verkehrsfachleute VSS. Retrieved 5 June 2024. "Guidelines for the
Bryan_Adey
American computer scientist (1953–1995)
Peter Franaszek, Gary Miller, Michael Rabin, Robert Solovay, and Volker Strassen, Yoav Freund and Robert Schapire, Gerard Holzmann, Robert Kurshan, Moshe
Paris_Kanellakis
Right tributary of Rhine river in Germany
ISBN 3-8313-1321-0 Heide Ringhand (1992), Die Binnenschiffahrt. Fliessende Strassen – Lebendige Ströme (in German), Velbert-Neviges: BeRing Verlag, p. 86,
Neckar
Highway designed for high-speed, regulated traffic flow
8 April 2014. Retrieved 7 April 2014. "Unfallentwicklung auf deutschen Straßen 2012" [Crashes on German Roads 2012] (PDF) (in German). Statistisches Bundesamt
Controlled-access_highway
STRASSEN ALGORITHM
STRASSEN ALGORITHM
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.
Boy/Male
Hindu, Indian, Marathi
With an Army of Gods
STRASSEN ALGORITHM
STRASSEN ALGORITHM
Girl/Female
Tamil
Chandhini | சாஂதீநீ
Moon light or a river, Star
Boy/Male
Hindu, Indian
Full Moon; Complete; Renewed
Boy/Male
Tamil
Lord Vishnu
Boy/Male
Hindu, Indian
Black Man
Girl/Female
Arabic, Australian, Christian, Farsi, Iranian, Muslim
Gazelle; Beautiful; A Plant
Male
Greek
(Îομική) Modern Greek name derived from the word nomikos, NOMIKI means "relating to the law."
Girl/Female
Hindu
Goddess Sita
Surname or Lastname
English
English : occupational name for a navigator, from Old Norse stýrimaðr ‘steersman’ (a compound of stýra ‘to steer’ + maðr ‘man’).English : from an Old French diminutive form Esturmin of a Germanic byname meaning ‘storm’. Compare Storm.North German (Sturmann) : altered spelling of Stuhrmann, an occupational name for a helmsman, from Middle Low German stūren ‘to steer’ + mann ‘man’.Jewish (eastern Ashkenazic) : origin uncertain; possibly an ornamental name from Polish szturman ‘mate (of a ship)’.
Boy/Male
British, English
From the Linden Tree Ford
Biblical
Jannes, who speaks or answers; afflicted; poor
STRASSEN ALGORITHM
STRASSEN ALGORITHM
STRASSEN ALGORITHM
STRASSEN ALGORITHM
STRASSEN ALGORITHM
p. pr. & vb. n.
of Straiten
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.
n.
The art of calculating by nine figures and zero.
v. t.
Figuratively: To cramp; to straiten; to oppress; to starve; to distress; as, to be pinched for money.
a.
To press together; to crowd; to straiten; to confine closely.
v.
To straiten; to distress; as, to be pressed with want or hunger.
v. t.
A variant of Straiten.
v. t.
See Straiten.
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.
To draw tighter; to straiten; to make more close in any manner.
v. t.
To make tense, or tight; to tighten.
n.
A highly refractive vitreous composition, variously colored, used in making imitations of precious stones or gems. See Strass.
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.
The art of calculating with any species of notation; as, the algorithms of fractions, proportions, surds, etc.
n.
Alt. of Algorithm
v. t.
To make strait; to make narrow; hence, to contract; to confine.