Search results
Results From The WOW.Com Content Network
The condition number is derived from the theory of propagation of uncertainty, and is formally defined as the value of the asymptotic worst-case relative change in output for a relative change in input. The "function" is the solution of a problem and the "arguments" are the data in the problem. The condition number is frequently applied to ...
Iterative algorithm. 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: Input: matrices A ...
The result matrix has the number of rows of the first and the number of columns of the second matrix. In mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in ...
In mathematics, and in particular linear algebra, the Moore–Penrose inverse of a matrix , often called the pseudoinverse, is the most widely known generalization of the inverse matrix. [ 1 ] It was independently described by E. H. Moore in 1920, [ 2 ] Arne Bjerhammar in 1951, [ 3 ] and Roger Penrose in 1955. [ 4 ]
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.
The number of additions and multiplications required in the Strassen algorithm can be calculated as follows: let () be the number of operations for a matrix. Then by recursive application of the Strassen algorithm, we see that f ( n ) = 7 f ( n − 1 ) + l 4 n {\displaystyle f(n)=7f(n-1)+l4^{n}} , for some constant l {\displaystyle l} that ...
Freivalds' algorithm (named after Rūsiņš Mārtiņš Freivalds) is a probabilistic randomized algorithm used to verify matrix multiplication. Given three n × n matrices , , and , a general problem is to verify whether . A naïve algorithm would compute the product explicitly and compare term by term whether this product equals .
Preconditioner. In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing a condition number of the problem.