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The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
In linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm for matrix multiplication.It is faster than the standard matrix multiplication algorithm for large matrices, with a better asymptotic complexity, although the naive algorithm is often better for smaller matrices.
Matrix chain multiplication (or the matrix chain ordering problem [1]) is an optimization problem concerning the most efficient way to multiply a given sequence of matrices. ...
In theoretical computer science, the computational complexity of matrix multiplication dictates how quickly the operation of matrix multiplication can be performed. Matrix multiplication algorithms are a central subroutine in theoretical and numerical algorithms for numerical linear algebra and optimization, so finding the fastest algorithm for matrix multiplication is of major practical ...
The Hadamard product operates on identically shaped matrices and produces a third matrix of the same dimensions. In mathematics, the Hadamard product (also known as the element-wise product, entrywise product [1]: ch. 5 or Schur product [2]) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.
Projection method (fluid dynamics) — computational fluid dynamics method; Reactive transport modeling in porous media — modeling of chemical reactions and fluid flow through the Earth's crust; Richard S. Varga — developed matrix splitting; Strang splitting — specific numerical method for solving differential equations using operator ...
Matrix multiplication; Polynomial evaluation (e.g., with Horner's rule) Newton's method for evaluating functions (from the inverse function) Convolutions and artificial neural networks; Multiplication in double-double arithmetic; Fused multiply–add can usually be relied on to give more accurate results.
Another method of multiplication is called Toom–Cook or Toom-3. The Toom–Cook method splits each number to be multiplied into multiple parts. The Toom–Cook method is one of the generalizations of the Karatsuba method. A three-way Toom–Cook can do a size-3N multiplication for the cost of five size-N multiplications. This accelerates the ...