数值分析
The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor f. To date, the captured flow friction factor f can be extracted from the…
The class of non-rigid registration methods proposed in the framework of PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting family of physically meaningful diffeomorphic registration methods.…
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
We present an efficient multi-accuracy algorithm for the computations of a set of special functions of a complex argument, z=x+iy. These functions include the complex probability function w(z), and closely related functions such as the…
We introduce an application for executing and testing different unconstrained optimization algorithms. The application contains a library of various test functions with pre-defined starting points. A several known classes of methods as well…
Total Variation (TV) is an effective and popular prior model in the field of regularization-based image processing. This paper focuses on total variation for removing impulse noise in image restoration. This type of noise frequently arises…
We propose a novel block-row partitioning method in order to improve the convergence rate of the block Cimmino algorithm for solving general sparse linear systems of equations. The convergence rate of the block Cimmino algorithm depends on…
Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many…
This work is devoted to the design of interior penalty discontinuous Galerkin (dG) schemes that preserve maximum principles at the discrete level for the steady transport and convection-diffusion problems and the respective transient…
In this paper, we consider recovering the signal $\bm{x}\in\mathbb{R}^{n}$ from its few noisy measurements $\bm{b}=A\bm{x}+\bm{z}$, where $A\in\mathbb{R}^{m\times n}$ with $m\ll n$ is the measurement matrix, and $\bm{z}\in\mathbb{R}^{m}$ is…
We present a systematic global sensitivity analysis using the Sobol method which can be utilized to rank the variables that affect two quantity of interests -- pore pressure depletion and stress change -- around a hydraulically-fractured…
A flexible and effective algorithm for complex roots and poles finding is presented. A wide class of analytic functions can be analyzed, and any arbitrarily shaped search region can be considered. The method is very simple and intuitive. It…
This note presents fast Cholesky/LU/QR decomposition algorithms with $O(n^{2.529})$ time complexity when using the fastest known matrix multiplication. The algorithms have potential application, since a quickly made implementation using…
The approximate joint diagonalization of a set of matrices consists in finding a basis in which these matrices are as diagonal as possible. This problem naturally appears in several statistical learning tasks such as blind signal…
The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high…
Tensor train (TT) decomposition has drawn people's attention due to its powerful representation ability and performance stability in high-order tensors. In this paper, we propose a novel approach to recover the missing entries of incomplete…
Elementary function calls are a common feature in numerical programs. While their implementions in library functions are highly optimized, their computation is nonetheless very expensive compared to plain arithmetic. Full accuracy is,…
Low-rank matrix approximation plays an increasingly important role in signal and image processing applications. This paper presents a new rank-revealing decomposition method called randomized rank-revealing UZV decomposition (RRR-UZVD).…
The call for efficient computer architectures has introduced a variety of application-specific compute engines to the heterogeneous computing landscape. One particular engine, the analog mesh computer, has been well received due to its…
Objective: To present the first real-time a posteriori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a…