Multivariate Polynomial Multiplication on GPU

Fast polynomial multiplication on a GPU

We present CUDA implementations of Fast Fourier Transforms over finite fields. This allows us to develop GPU support for dense univariate polynomial multiplication leading to speedup factors in the range 21 − 37 with respect to the best serial C-code available to us, for our largest input data sets. Since dense univariate polynomial multiplication is a core routine in symbolic computation, this...

Iterative Karatsuba For Multivariate Polynomial Multiplication

This work deals with Karatsuba method for multivariate polynomials, not recursing on variables number, but using an iterative scheme, with an eye to a better parallelism exploitation. Integers base 2 and 3 expansions are used in order to access the needed data. AMS Subject Classification: 11A05, 11A25, 11K65, 11Y70

On multivariate polynomial interpolation

We provide a map Θ 7→ ΠΘ which associates each finite set Θ of points in C with a polynomial space ΠΘ from which interpolation to arbitrary data given at the points in Θ is possible and uniquely so. Among all polynomial spaces Q from which interpolation at Θ is uniquely possible, our ΠΘ is of smallest degree. It is also Dand scale-invariant. Our map is monotone, thus providing a Newton form for...

Plain Polynomial Arithmetic on GPU

As for serial code on CPUs, parallel code on GPUs for dense polynomial arithmetic relies on a combination of asymptotically fast and plain algorithms. Those are employed for data of large and small size, respectively. Parallelizing both types of algorithms is required in order to achieve peak performances. In this paper, we show that the plain dense polynomial multiplication can be efficiently ...

Sparse Matrix-Vector Multiplication on a GPU