Generalized Givens Rotations Applied to Complex Joint Eigenvalue Decomposition

This paper shows the different ways of using generalized Givens rotations in complex joint eigenvaluedecomposition (JEVD) problem. It presents the different schemes of generalized Givens rotation, justifies the introducedapproximations and focuses on the process of extending an algorithm developed for real JEVD to the complex JEVD.Several Joint Diagonalization problem use generalized Givens rotations to achieve the solution, many algorithmsdeveloped in the real case exist in the literature and are not generalized to the complex case. Hence, we show herein asimple and not trivial way to get the complex case from the real one. Simulation results are provided to highlight theeffectiveness and behaviour of the proposed techniques for different scenarios.

Pruning Multilayered ELM Using Cholesky Factorization and Givens Rotation Transformation

Extreme learning machine is originally proposed for the learning of the single hidden layer feedforward neural network to overcome the challenges faced by the backpropagation (BP) learning algorithm and its variants. Recent studies show that ELM can be extended to the multilayered feedforward neural network in which the hidden node could be a subnetwork of nodes or a combination of other hidden nodes. Although the ELM algorithm with multiple hidden layers shows stronger nonlinear expression ability and stability in both theoretical and experimental results than the ELM algorithm with the single hidden layer, with the deepening of the network structure, the problem of parameter optimization is also highlighted, which usually requires more time for model selection and increases the computational complexity. This paper uses Cholesky factorization strategy and Givens rotation transformation to choose the hidden nodes of MELM and obtains the number of nodes more suitable for the network. First, the initial network has a large number of hidden nodes and then uses the idea of ridge regression to prune the nodes. Finally, a complete neural network can be obtained. Therefore, the ELM algorithm eliminates the need to manually set nodes and achieves complete automation. By using information from the previous generation’s connection weight matrix, it can be evitable to re-calculate the weight matrix in the network simplification process. As in the matrix factorization methods, the Cholesky factorization factor is calculated by Givens rotation transform to achieve the fast decreasing update of the current connection weight matrix, thus ensuring the numerical stability and high efficiency of the pruning process. Empirical studies on several commonly used classification benchmark problems and the real datasets collected from coal industry show that compared with the traditional ELM algorithm, the pruning multilayered ELM algorithm proposed in this paper can find the optimal number of hidden nodes automatically and has better generalization performance.

Design and VLSI Implementation of a Reduced-Complexity Sorted QR Decomposition for High-Speed MIMO Systems

In this article, a low-complexity and high-throughput sorted QR decomposition (SQRD) for multiple-input multiple-output (MIMO) detectors is presented. To reduce the heavy hardware overhead of SQRD, we propose an efficient SQRD algorithm based on a novel modified real-value decomposition (RVD). Compared to the latest study, the proposed SQRD algorithm can save the computational complexity by more than 44.7% with similar bit error rate (BER) performance. Furthermore, a corresponding deeply pipelined hardware architecture implemented with the coordinate rotation digital computer (CORDIC)-based Givens rotation (GR) is designed. In the design, we propose a time-sharing Givens rotation structure utilizing CORDIC modules in idle state to share the concurrent GR operations of other CORDIC modules, which can further reduce hardware complexity and improve hardware efficiency. The proposed SQRD processor is implemented in SMIC 55-nm CMOS technology, which processes 62.5 M SQRD per second at a 250-MHz operating frequency with only 176.5 kilo-gates. Compared to related studies, the proposed design has the best normalized hardware efficiency and achieves a 6-Gbps MIMO data rate which can support current high-speed wireless communication systems such as IEEE 802.11ax.

Hartree-Fock on a superconducting qubit quantum computer

The simulation of fermionic systems is among the most anticipated applications of quantum computing. We performed several quantum simulations of chemistry with up to one dozen qubits, including modeling the isomerization mechanism of diazene. We also demonstrated error-mitigation strategies based on N-representability that dramatically improve the effective fidelity of our experiments. Our parameterized ansatz circuits realized the Givens rotation approach to noninteracting fermion evolution, which we variationally optimized to prepare the Hartree-Fock wave function. This ubiquitous algorithmic primitive is classically tractable to simulate yet still generates highly entangled states over the computational basis, which allowed us to assess the performance of our hardware and establish a foundation for scaling up correlated quantum chemistry simulations.

Combining sign and parametric restrictions in SVARs by utilising Givens rotations

This paper shows how to impose parametric restrictions in conjunction with sign restrictions to separate the shocks in SVARs. In sign restrictions, it is common to rotate an initial set of orthogonal shocks by utilising a Givens rotation matrix. In this paper, we show how to construct the Givens rotation matrix when parametric restrictions are part of the identification in sign restricted SVARs. The properties of Givens matrices are such that the parametric restrictions imply a system of equations which can be solved for the unknown parameters (or “angles”) in a rotation matrix, conditional on the values of the parameters which are drawn. The Givens rotation matrix formed in this manner is such that the parametric restrictions on the impulse responses are satisfied on each draw in sign restrictions. The method is demonstrated in an influential SVAR and is shown to generate results similar to those from a recent method which imposes the orthogonality and zero parametric restrictions on the columns of the rotation matrix in sign restrictions.

Hardware Architectures of the QR-Decomposition Based on a Givens Rotation Technique

The fixed-point hardware architecture of the QR decomposition is constrained by a several issues that leads to decrease of a compute accuracy depending on a matrix size. In this article described the hardware architectures based on CORDIC algorithm and approximation functions. As a basis technique is used a Givens rotation technique, because it is a most suitable technique for hardware implementation