相关论文: Comparison of Multi-quark Matrix Inversion Algorit…
This talk presents results of a comparitive study of iterative algorithms like minimal residue ($MR$) and conjugate gradient ($CG$, $BiCG\gamma_5$, and \bicgstab) used for inverting the Dirac matrix $M$. The tests were done on the…
In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…
The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider…
An algorithm for the numerical inversion of large matrices, the biconjugate gradient algorithm (BGA), is investigated in view of its use for Monte Carlo simulations of fermionic field theories. It is compared with the usual conjugate…
The computational effort in the calculation of Wilson fermion quark propagators in Lattice Quantum Chromodynamics can be considerably reduced by exploiting the Wilson fermion matrix structure in inversion algorithms based on the…
We examine some numerical iterative methods for computing the eigenvalues and eigenvectors of real matrices. The five methods examined here range from the simple power iteration method to the more complicated QR iteration method. The…
In this paper, we present the QR Algorithm with Permutations that shows an improved convergence rate compared to the classical QR algorithm. We determine a bound for performance based on best instantaneous convergence, and develop low…
Graphical Processing Units (GPUs) are more and more frequently used for lattice QCD calculations. Lattice studies often require computing the quark propagators for several masses. These systems can be solved using multi-shift inverters but…
Estimation of actual errors from the residue in iterative solutions is necessary for efficient solution of large problems when their condition number is much larger than one. Such estimators for conjugate gradient algorithms used to solve…
In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time's spending. Further, both of…
This work presents a novel approach to compute the eigenvalues of non-Hermitian matrices using an enhanced shifted QR algorithm. The existing QR algorithms fail to converge early in the case of non-hermitian matrices, and our approach shows…
We compare different conjugate gradient -- like matrix inversion methods (CG, BiCGstab1 and BiCGstab2) employing for this purpose the compact lattice quantum electrodynamics (QED) with Wilson fermions. The main goals of this investigation…
Matrix multiplication is the dominant computation during Machine Learning (ML) inference. To efficiently perform such multiplication operations, Compute-in-memory (CiM) paradigms have emerged as a highly energy efficient solution. However,…
Factorizing large matrices by QR with column pivoting (QRCP) is substantially more expensive than QR without pivoting, owing to communication costs required for pivoting decisions. In contrast, randomized QRCP (RQRCP) algorithms have proven…
Parallel tempering simulates at many quark masses simultaneously, by changing the mass during the simulation while remaining in equilibrium. The algorithm is faster than pure HMC if more than one mass is needed, and works better the smaller…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
Obtaining the inverse of a large symmetric positive definite matrix $\mathcal{A}\in\mathbb{R}^{p\times p}$ is a continual challenge across many mathematical disciplines. The computational complexity associated with direct methods can be…
Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also…
The computation of generalized inverses of quaternion matrices is a fundamental problem in quaternion linear algebra, with wide-ranging applications in signal processing, image restoration, and multidimensional data analysis. This paper…
We analyse some QR decomposition algorithms, and show that the I/O complexity of the tile based algorithm is asymptotically the same as that of matrix multiplication. This algorithm, we show, performs the best when the tile size is chosen…