Non-zero element of a matrix selected by an algorithm
This article is about pivots in matrices. For the pivot in the quicksort algorithm, see Quicksort.
The pivot or pivot element is the element of a matrix, or an array, which is selected first by an algorithm (e.g. Gaussian elimination, simplex algorithm, etc.), to do certain calculations. In the case of matrix algorithms, a pivot entry is usually required to be at least distinct from zero, and often distant from it; in this case finding this element is called pivoting. Pivoting may be followed by an interchange of rows or columns to bring the pivot to a fixed position and allow the algorithm to proceed successfully, and possibly to reduce round-off error. It is often used for verifying row echelon form.
Pivoting might be thought of as swapping or sorting rows or columns in a matrix, and thus it can be represented as multiplication by permutation matrices. However, algorithms rarely move the matrix elements because this would cost too much time; instead, they just keep track of the permutations.
Overall, pivoting adds more operations to the computational cost of an algorithm. These additional operations are sometimes necessary for the algorithm to work at all. Other times these additional operations are worthwhile because they add numerical stability to the final result.
The pivot or pivotelement is the element of a matrix, or an array, which is selected first by an algorithm (e.g. Gaussian elimination, simplex algorithm...
Quicksort is a divide-and-conquer algorithm. It works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays...
Look up pivot, pivoting, or pivots in Wiktionary, the free dictionary. Pivot may refer to: Pivot, the point of rotation in a lever system More generally...
implemented as a pivot operation. First, a nonzero pivotelement is selected in a nonbasic column. The row containing this element is multiplied by its...
used to supply a good pivot for an exact selection algorithm, most commonly quickselect, that selects the kth smallest element of an initially unsorted...
choosing one element as a pivot and partitioning the data in two based on the pivot, accordingly as less than or greater than the pivot. However, instead...
cavity during a single visit. It often includes a protective element called a ferrule. Pivot teeth were developed to shorten the execution cycle and skip...
pivoting in Wiktionary, the free dictionary. Pivoting may refer to: The act of finding a pivotelement A type of computer security exploit Pivoting (TV...
last element as pivot) this occurs for sorted data, which is a common case. The most complex issue in quicksort is thus choosing a good pivotelement, as...
optimize this effect, Sij should be the off-diagonal element with the largest absolute value, called the pivot. The Jacobi eigenvalue method repeatedly performs...
selection are based on choosing a special "pivot" element from the input, and using comparisons with this element to divide the remaining n − 1 {\displaystyle...
randrange(1, n) # Will take a random number in the range 1~n X = A[i] # The pivotelement """Partition A into elements < x, x, and >x # as shown in the figure...
For example, we might swap rows to perform partial pivoting, or we might do it to set the pivotelement a n , n {\displaystyle a_{n,n}} on the main diagonal...
there exists i: l_i < r_i do // pick PivotElement in S_j[l_j], .., S_j[r_j], chose random j uniformly v := pickPivot(S, l, r) for i = 1 to p do m_i = binarySearch(v...
computational method for Kalman decomposition, which is based on the pivotelement method. A variant of Rosenbrock’s method is implemented in the minreal...
is partitioned. The simplest pivot selection algorithm is to take the first or the last element of the list as the pivot, causing poor behavior for the...
computing the transpose of a matrix without using much additional storage Pivotelement — entry in a matrix on which the algorithm concentrates Matrix-free...
identifies a pivotelement in the list and then partitions the list into two sublists, those elements less than the pivot and those greater than the pivot. Spreadsort...
and the weighted median is the element corresponding to the weight 0.3, which is 4. The weights on each side of the pivot add up to 0.45 and 0.25, satisfying...
5)}}} There is one non-ancestor node using the variable 1 as a pivotelement: C3{\displaystyle C_{3}}. (1)(2)(1)C1(1,3)C2(−1,2,5)C3(2,3,5)C4(1,−2)C7(1...
partition step is massively parallel (each input element should be compared to a chosen pivotelement) and the two recursive calls can be performed in...
Osmium (from Ancient Greek ὀσμή (osmḗ) 'smell') is a chemical element; it has symbol Os and atomic number 76. It is a hard, brittle, bluish-white transition...
Kidd Pivot (known from 2010 to 2012 as Kidd Pivot Frankfurt RM), is a contemporary dance theatre company based in Vancouver, Canada. The company, currently...
eigenvalues and pivots resulting from application of the mixed method. Olek C Zienkiewicz, Robert L Taylor and J.Z. Zhu. The Finite Element Method: Its Basis...
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