You must implement a discrete 1D convolution of a data array A and a filter array F. Both sequential and parallel programs must be provided. Both programs must be based on the same algorithm, i.e. the ...

$$u(x_i) = \sum_{j=1}^{N_S} K(x_i, y_j) \rho_j,\quad \text{for~} i = 1, \ldots, N_T$$ The DMK (dual-space multilevel kernel-splitting) framework uses a hierarchy of ...

A new computational method for solving the fifth order Korteweg-de Vries (fKdV) equation is proposed. The nonlinear partial differential equation is discretized in space using the discrete singular ...

Abstract: A fast linear convolution algorithm based on the Discrete Hirschman Transform (DHT) has been developed recently. It performs better than the traditional convolution based on the Discrete ...

Abstract: A new, computationally efficient, algorithm for linear convolution is proposed. This algorithm uses an N point instead of the usual 2N-1 point circular convolution to produce a linear ...

Our research proves a conjecture from string theory asserting the vanishing of a specific convolution sum arising in the 4-graviton scattering amplitude in 10-dimensional type IIB string theory. The ...