Pivot Element
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The pivot or pivot element is the element of a matrix, an array, or some other kind of finite set, which is selected first by an algorithm (e.g. Gaussian elimination, Quicksort, 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 co...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The pivot or pivot element is the element of a matrix, an array, or some other kind of finite set, which is selected first by an algorithm (e.g. Gaussian elimination, Quicksort, 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. 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.
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