◀ Prev · Parts · Full · Next ▶

layout: Wide · Narrow · Centered

Triangular arrays may list mathematical values other than numbers; for instance the Bell polynomials form a triangular array in which each array entry is a polynomial.cite-ref-10[10]

Arrays in which the length of each row grows as a linear function of the row number (rather than being equal to the row number) have also been considered.cite-ref-11[11]

Romberg's method can be used to estimate the value of a definite integral by completing the values in a triangle of numbers.cite-ref-12[12]

The Boustrophedon transform uses a triangular array to transform one integer sequence into another.cite-ref-13[13]

In general, a triangular array is used to store any table indexed by two natural numbers where j ≤ i.

Storing a triangular array in a computer requires a mapping from the two-dimensional coordinates (i, j) to a linear memory address. If two triangular arrays of equal size are to be stored (such as in LU decomposition), they can be combined into a standard rectangular array. If there is only one array, or it must be easily appended to, the array may be stored where row i begins at the ith triangular number Ti. Just like a rectangular array, one multiplication is required to find the start of the row, but this multiplication is of two variables (i*(i+1)/2), so some optimizations such as using a sequence of shifts and adds are not available.

◀ Prev · Parts · Full · Next ▶