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...\times n</math> [[Computational complexity of matrix multiplication|matrix multiplication]]. If only the distances between each pair of vertices are sought, the same ...tps://docs.scipy.org/doc/numpy/reference/generated/numpy.matrix.html numpy.matrix]). ...

* [[Algorithms]] * [[Computational complexity of matrix multiplication|Matrix multiplication]] ...

...in P. |last4=Ye |first4=Christopher |date=2024 |title=On the Complexity of Algorithms with Predictions for Dynamic Graph Problems |journal=Itcs '24 |pages=62:1–6 ...m is given an integer <math>n</math> and an <math>n\times n</math> Boolean matrix <math>M</math>. The algorithm then runs for <math>n</math> rounds, and at e ...

...e=Multi-Terminal Binary Decision Diagrams: An Efficient Data Structure for Matrix Representation |url=https://doi.org/10.1023/A:1008647823331 |journal=Formal == Matrix partitioning == ...

...th stemming from the fact that the rows and columns come from the original matrix (rather than left and right singular vectors): ...composed matrix are essentially the same as their meanings in the original matrix. ...

...019}}{{Short description|Description of limiting behavior in probabilistic algorithms}} ...thm for verifying matrix multiplication. It runs faster than deterministic algorithms WHP. ...

...te the [[determinant]] or the [[echelon form]] of a [[Matrix (mathematics)|matrix]] with [[integer]] entries using only integer arithmetic; any [[division (m ...al Bareiss algorithm is distinct from the Bareiss algorithm for [[Toeplitz matrix|Toeplitz matrices]]. ...

...rential equation]]s.<ref>{{cite journal|title=Efficient Algorithms for the Matrix Cosine and Sine|author=Gareth I. Hargreaves |author2=Nicholas J. Higham |jo ...trix|power]] of the matrix {{mvar|X}}, and {{mvar|I}} being the [[identity matrix]] of appropriate dimensions. ...

...known for his research on [[algorithm]]s for [[polynomial]]s and [[matrix multiplication]]. ...algorithms|computational complexity]] and has developed a number of new [[algorithms]]. One of his notable early results is a proof that the number of multiplic ...

'''Communication-avoiding algorithms''' minimize movement of data within a [[memory hierarchy]] for improving it A common computational model in analyzing communication-avoiding algorithms is the two-level memory model: ...

...e are [[algorithm]]s for the arithmetic operations (addition, subtraction, multiplication) and for the above problems may be called a '''computable ring''', or '''ef ...the syzygies problem for a single equation, then one may deduce from them algorithms for the similar problems concerning systems of equations.'' ...

...rt FFT operations on the columns and rows of the matrix, with a correction multiplication by "[[twiddle factor]]s" in between.{{sfn|Hart|Tornaría|Watkins|2010|p=191} # The data (in natural order) is first arranged into a matrix. ...

...tive]] "[[Logical conjunction|and]]"), or equivalently the set {0,1} under multiplication: the only [[semilattice]] with two elements and the only non-null semigroup ...l connective "[[exclusive or|xor]]"), or equivalently the set {−1,1} under multiplication: the only [[group (mathematics)|group]] of order two. ...

...-SVD algorithm, the <math>D</math> is first fixed and the best coefficient matrix <math>X</math> is found. As finding the truly optimal <math>X</math> is har ...blem by approximate the <math>E_k</math> term with a <math>rank -1</math> matrix using [[singular value decomposition]], then update <math>d_k</math> with i ...

...book|last=Hackbusch|first=Wolfgang|date=2015|title=Hierarchical matrices: Algorithms and Analysis|volume=49|publisher=Springer|doi=10.1007/978-3-662-47324-5|ser ...irst1=Wolfgang|last2=Khoromskij|first2=Boris N.|date=2000|title=A sparse H-Matrix Arithmetic. Part II: Application to Multi-Dimensional Problems|journal=Comp ...

...in particular [[Randomized algorithm#Derandomization|finding deterministic algorithms]] for PIT, is one of the most important open problems in algebraic computin ...s a black-box), we can confirm that the equality holds through brute-force multiplication and addition, but the [[time complexity]] of the brute-force approach grows ...

...bounded speedup of matrix multiplication. The memory requirement of matrix multiplication is roughly Thus the memory-bounded speedup is for matrix multiplication is: ...

{{about|a technique in the design of graph algorithms|the use of color to display information|color code||Color code (disambiguat ...theory|graph]]. The traditional color-coding algorithm is [[probabilistic algorithms|probabilistic]], but it can be [[Derandomization#Derandomization|derandomiz ...

{{Short description|Algorithmic runtime requirements for matrix multiplication}} {{unsolved|computer science|What is the fastest algorithm for matrix multiplication?}} ...

...ath>, non-negative integers <math>m,n</math>, and a [[Matrix (mathematics)|matrix]] <math>A\in\mathbb F^{m\times n}</math>, a '''rank decomposition''' or ''' ...hbf{a}_n\end{bmatrix}</math> is an <math display="inline">m\times n</math> matrix with <math display="inline">\mathbf{a}_j</math> as the <math display="inlin ...