数值分析
Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be…
The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n log n) instead of O(n 2) arithmetic operations. Graph Signal Processing (GSP) is a recent…
In many machine learning and data related applications, it is required to have the knowledge of approximate ranks of large data matrices at hand. In this paper, we present two computationally inexpensive techniques to estimate the…
We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought…
We provide numerical evidence demonstrating the necessity of employing a superparametric geometry representation in order to obtain optimal convergence orders on two-dimensional domains with curved boundaries when solving the Euler…
In this paper we present an efficient algorithm to compute the eigen decomposition of a matrix that is a weighted sum of the self outer products of vectors such as a covariance matrix of data. A well known algorithm to compute the eigen…
Finding the symmetric and orthogonal decomposition (SOD) of a tensor is a recurring problem in signal processing, machine learning and statistics. In this paper, we review, establish and compare the perturbation bounds for two natural types…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
An accurate implicit description of geometries is enabled by the level-set method. Level-set data is given at the nodes of a higher-order background mesh and the interpolated zero-level sets imply boundaries of the domain or interfaces…
A machine-learning-based framework for modeling the error introduced by surrogate models of parameterized dynamical systems is proposed. The framework entails the use of high-dimensional regression techniques (e.g., random forests, LASSO)…
Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also…
The problem of increasing the accuracy of an approximate solution is considered for boundary value problems for parabolic equations. For ordinary differential equations (ODEs), nonstandard finite difference schemes are in common use for…
We present a cache-oblivious adaptation of matrix multiplication to be incorporated in the parallel TU decomposition for rectangular matrices over finite fields, based on the Morton-hybrid space-filling curve representation. To realise…
This paper is concerned with approximating the dominant left singular vector space of a real matrix $A$ of arbitrary dimension, from block Krylov spaces generated by the matrix $AA^T$ and the block vector $AX$. Two classes of results are…
An iteration-free method of domain decomposition is considered for approximate solving a boundary value problem for a second-order parabolic equation. A standard approach to constructing domain decomposition schemes is based on a partition…
The big data era is swamping areas including data analysis, machine/deep learning, signal processing, statistics, scientific computing, and cloud computing. The multidimensional feature and huge volume of big data put urgent requirements to…
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks…
The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models…