30 citations · 85 across the 15 of their papers we have counts for
15 papers
Quantum radial basis function methods for scattered data fitting
Lingxia Cui, Hua Xiang
Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be h…
A quantum-inspired algorithm for approximating statistical leverage scores
Qian Zuo, Hua Xiang
Suppose a matrix of rank with singular value decomposition , where , $V_{A} \in \ma…
Incompatibility probability of random quantum measurements
Lin Zhang, Hua Xiang, Xianqing Li-Jost +1
Incompatibility of quantum measurements is of fundamental importance in quantum mechanics. It is closely related to many nonclassical phenomena such as Bell nonlocality, quantum un…
Quantum algorithm for total least squares data fitting
Hefeng Wang, Hua Xiang
The total least squares~(TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors,…
Randomized Row and Column Iterative Methods with a Quantum Computer
Changpeng Shao, Hua Xiang
We consider the quantum implementations of the two classical iterative solvers for a system of linear equations, including the Kaczmarz method which uses a row of coefficient matri…
Quantum Regularized Least Squares Solver with Parameter Estimate
Changpeng Shao, Hua Xiang
In this paper we propose a quantum algorithm to determine the Tikhonov regularization parameter and solve the ill-conditioned linear equations, for example, arising from the finite…
Randomized QLP algorithm and error analysis
Nianci Wu, Hua Xiang
In this paper, we describe the randomized QLP (RQLP) algorithm and its enhanced version (ERQLP) for computing the low rank approximation to of size efficiently such…
Singular Values of Riemann Curvature Tensor
Xiaokai He, Hua Xiang
We introduce the concept of singular values for the Riemann curvature tensor, a central mathematical tool in Einstein's theory of general relativity. We study the properties relate…
Quantum Circulant Preconditioner for Linear System of Equations
Changpeng Shao, Hua Xiang
We consider the quantum linear solver for with the circulant preconditioner . The main technique is the singular value estimation (SVE) introduced in [I. Kerenidis and A.…
M-eigenvalues of The Riemann Curvature Tensor
Hua Xiang, Liqun Qi, Yimin Wei
The Riemann curvature tensor is a central mathematical tool in Einstein's theory of general relativity. Its related eigenproblem plays an important role in mathematics and physics.…
On the M-eigenvalues of elasticity tensor and the strong ellipticity condition
Hua Xiang, Liqun Qi, Yimin Wei
Strong ellipticity is an important property in the elasticity theory. In 2009, M-eigenvalues were introduced for the elasticity tensor. It was shown that M-eigenvalues are invarian…
Preconditioners and Their Analyses for Edge Element Saddle-point Systems Arising from Time-harmonic Maxwell Equations
Hua Xiang, Shiyang Zhang, Jun Zou
We shall propose and analyze some new preconditioners for the saddle-point systems arising from the edge element discretization of the time-harmonic Maxwell equations in three dime…
Adaptive Uzawa algorithm for nonsymmetric generalized saddle point problem
Hailun Shen, Hua Xiang
In this paper, we extend the inexact Uzawa algorithm in [Q. Hu, J. Zou, SIAM J. Matrix Anal., 23(2001), pp. 317-338] to the nonsymmetric generalized saddle point problem. The techn…
An Inexact Uzawa Algorithm for Generalized Saddle-Point Problems and Its Convergence
Kazufumi Ito, Hua Xiang, Jun Zou
We propose an inexact Uzawa algorithm with two variable relaxation parameters for solving the generalized saddle-point system. The saddle-point problems can be found in a wide clas…
Perturbation Analysis and Randomized Algorithms for Large-Scale Total Least Squares Problems
Pengpeng Xie, Yimin Wei, Hua Xiang
In this paper, we present perturbation analysis and randomized algorithms for the total least squares (TLS) problems. We derive the perturbation bound and check its sharpness by nu…