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#REDIRECT [[Matrix multiplication algorithm#Sub-cubic algorithms]] ...

...the [[Computational complexity of matrix multiplication|best known matrix multiplication algorithm]] runs in <math>O(n^{2.3729})</math> time.<ref name="williams">{{ |title=Randomized algorithms ...

{{Short description|German mathematician and algorithms researcher (b.1936)}} ...inal and influential contributions to the design and analysis of efficient algorithms."<ref name=sigact2008 /> ...

{{Short description|Matrix generating a linear code}} {{For|generator matrices in probability theory|transition rate matrix}} ...

...[[software library]] for manipulating [[Vector (geometric)|vectors]] and [[Matrix (computer science)|matrices]] in [[C++]] created by the U.S. [[National Ins ...TNT is analogous to the [[BLAS]] library used by [[LAPACK]]. Higher level algorithms, such as [[LU decomposition]] and [[singular value decomposition]], are pro ...

...lished by [[Springer Science+Business Media|Springer]] as volume 19 of the Algorithms and Computations in Mathematics series.<ref>{{Cite web|url=http://magma.mat : Magma includes [[permutation group|permutation]], [[matrix (mathematics)|matrix]], [[finitely presented group|finitely presented]], [[solvable group|solubl ...

...y]] with different levels of cache having different sizes. Cache-oblivious algorithms are contrasted with explicit ''[[loop tiling]]'', which explicitly breaks a ...arly optimal performance in an absolute sense. The goal of cache-oblivious algorithms is to reduce the amount of such tuning that is required. ...

== Example: matrix-vector multiplication == The following is an example of matrix vector multiplication. There are three arrays, each with 100 elements. The code does not partitio ...

...algorithm'' (Tolimieri et al., 1997),<ref>R. Tolimieri, M. An, and C.Lu, ''Algorithms for Discrete Fourier Transform and Convolution'', Springer-Verlag, 2nd ed., ...th a circulant matrix is equivalent to the [[cyclic convolution]] with the matrix's row vector. This relation is an example of the fact that the [[multiplica ...

...omplexity, and [[Stephen Cook]], who cleaned the description of it, is a [[multiplication algorithm]] for large integers. ...iplication sub-operations can then be computed recursively using Toom–Cook multiplication again, and so on. Although the terms "Toom-3" and "Toom–Cook" are sometimes ...

{{Short description|Matrix with shifting rows}} ...eft to right is constant. For instance, the following matrix is a Toeplitz matrix: ...

...ges |first=Uzi |last=Vishkin |publisher=Class notes of courses on parallel algorithms taught since 1992 at the University of Maryland, College Park, Tel Aviv Uni ...en referred to as "[[sequential algorithm]]s", by contrast with concurrent algorithms. ...

{{Short description|Kind of square matrix in linear algebra}} ...low the first [[diagonal#Matrices|subdiagonal]], and a '''lower Hessenberg matrix''' has zero entries above the first [[Diagonal#Matrices|superdiagonal]].<re ...

{{Short description|Discrete fourier transform expressed as a matrix}} ...transformation matrix]], which can be applied to a signal through [[matrix multiplication]]. ...

...''perform'' the multiplications, but merely to decide the sequence of the matrix multiplications involved. The problem may be solved using [[dynamic progra There are many options because matrix multiplication is [[associativity|associative]]. In other words, no matter how the product ...

{{Short description|Recursive algorithm for matrix multiplication}} {{distinguish|text=the [[Schönhage–Strassen algorithm]] for multiplication of polynomials}} ...

The following discussion assumes an elementary knowledge of [[matrix (mathematics)|matrices]]. ...26. To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption. ...

...ns of the matrix elements. If <math>A</math> is an <math>n \times n</math> matrix, where <math>a_{ij}</math> is the entry in the <math>i</math>-th row and <m ...o [[Matrix multiplication algorithm|matrix multiplication]], but most such algorithms are not practical. ...

...tion of algorithms, in addition to comparisons, then asymptotically faster algorithms may be possible. For example, if it is known that the {{mvar|N}} objects ar ...it by more than a constant factor. For this reason, asymptotically optimal algorithms are often seen as the "end of the line" in research, the attaining of a res ...

..._k= \|(A - \mu I)^{-1}b_k \|. </math> Since eigenvectors are defined up to multiplication by constant, the choice of <math>C_k</math> can be arbitrary in theory; pra At every iteration, the vector <math>b_k</math> is multiplied by the matrix <math>(A - \mu I)^{-1}</math> and normalized. ...