Arens multiplication and convolution

Tight Cell-Probe Bounds for Online Integer Multiplication and Convolution

We show tight bounds for both online integer multiplication and convolution in the cell-probe model with word size w. For the multiplication problem, one pair of digits, each from one of two n digit numbers that are to be multiplied, is given as input at step i. The online algorithm outputs a single new digit from the product of the numbers before step i + 1. We give a Θ (

Convolution-multiplication identities for Tutte polynomials of matroids

Abstract. We give a general multiplication-convolution identity for the multivariate and bivariate rank generating polynomial of a matroid. The bivariate rank generating polynomial is transformable to and from the Tutte polynomial by simple algebraic operations. Several identities, almost all already known in some form, are specialization of this identity. Combinatorial or probabilistic interpr...

Multiplication Algorithm of Large Integers using Finite Discrete Convolution

Several existing algorithms for multiplication of large integers are discussed, and a highly efficient algorithm based on finite discrete convolution is introduced. In the new algorithm, large integers are split into many digits and stored in arrays, every item in array stands for every digit of large integer. In this way, the integer can be any large; the only limit is the memory of computer. ...

Multiplication Symmetric Convolution Property for Discrete Trigonometric Transforms

The symmetric-convolution multiplication (SCM) property of discrete trigonometric transforms (DTTs) based on unitary transform matrices is developed. Then as the reciprocity of this property, the novel multiplication symmetric-convolution (MSC) property of discrete trigonometric transforms, is developed.

Convolution and Homogeneous Spaces