Related papers: Computing matrix inversion with optical networks
Interpreting spectropolarimetric observations of the solar atmosphere takes much longer than the acquiring the data. The most important reason for this is that the model fitting, or "inversion", used to infer physical quantities from the…
Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is…
This study focuses on inverting time-domain airborne electromagnetic data in 2D by training a neural-network to understand the relationship between data and conductivity, thereby removing the need for expensive forward modeling during the…
One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse…
Linear detectors such as zero forcing (ZF) or minimum mean square error (MMSE) are imperative for large/massive MIMO systems for both the downlink and uplink scenarios. However these linear detectors require matrix inversion which is…
Volker Strassen first suggested an algorithm to multiply matrices with worst case running time less than the conventional $\mathcal{O}(n^3)$ operations in 1969. He also presented a recursive algorithm with which to invert matrices, and…
Reconfigurable linear optical networks are a key component for the development of optical quantum information processing platforms in the NISQ era and beyond. We report the implementation of such a device based on an innovative design that…
Modern microelectronic processors have migrated towards parallel computing architectures with many-core processors. However, such expansion comes with diminishing returns exacted by the high cost of data movement between individual…
The rapid advancements in machine learning across numerous industries have amplified the demand for extensive matrix-vector multiplication operations, thereby challenging the capacities of traditional von Neumann computing architectures. To…
This paper deals with circulant matrices. It is shown that a circulant matrix can be multiplied by a vector in time O(n log(n)) in a ring with roots of unity without making use of an FFT algorithm. With our algorithm we achieve a speedup of…
With its unique parallel processing capability, optical neural network has shown low-power consumption in image recognition and speech processing. At present, the manufacturing technology of programmable photonic chip is not mature, and the…
We improve the current best running time value to invert sparse matrices over finite fields, lowering it to an expected $O\big(n^{2.2131}\big)$ time for the current values of fast rectangular matrix multiplication. We achieve the same…
In this paper, we compose a computational algorithm for the determinant and the inverse of the n x n cyclic nonadiagonal matrix. The algorithm is suited for implementation using computer algebra systems (CAS) such as Mathematica and Maple.
A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 by 2 matrix using both the formula and a Monte Carlo calculation are compared. A prescription is given to determine when a matrix with…
We present RXTX, a new algorithm for computing the product of matrix by its transpose $XX^{t}$ for $X\in \mathbb{R}^{n\times m}$. RXTX uses $5\%$ fewer multiplications and $5\%$ fewer operations (additions and multiplications) than…
The {\it matrix-chain multiplication} problem is a classic problem that is widely taught to illustrate dynamic programming. The textbook solution runs in $\theta(n^3)$ time. However, there is a complex $O(n \log n)$-time method \cite{HU82},…
Integrated photonics computing has emerged as a promising approach to overcome the limitations of electronic processors in the post-Moore era, capitalizing on the superiority of photonic systems. However, present integrated photonics…
The escalating demands of compute-intensive applications urgently necessitate the adoption of optical interconnect technologies to overcome bottlenecks in scaling computing systems. This requires fully exploiting the inherent parallelism of…
3D detailed radiative transfer is computationally taxing, since the solution of the radiative transfer equation involves traversing the six dimensional phase space of the 3D domain. With modern supercomputers the hardware available for…
Optical neural networks (ONNs), or optical neuromorphic hardware accelerators, have the potential to dramatically enhance the computing power and energy efficiency of mainstream electronic processors, due to their ultralarge bandwidths of…