Related papers: Parallel Matrix Function Evaluation via Initial va…
To design efficient parallel algorithms, some recent papers showed that many sequential iterative algorithms can be directly parallelized but there are still challenges in achieving work-efficiency and high-parallelism. Work-efficiency can…
Parallel-in-time integration has been the focus of intensive research efforts over the past two decades due to the advent of massively parallel computer architectures and the scaling limits of purely spatial parallelization. Various…
In this contribution the usage of the Parareal method is proposed for the time-parallel solution of the eddy current problem. The method is adapted to the particular challenges of the problem that are related to the differential algebraic…
In the near future, massively parallel computing systems will be necessary to solve computation intensive applications. The key bottleneck in massively parallel implementation of numerical algorithms is the synchronization of data across…
We initiate the study of matroid problems in a new oracle model called dynamic oracle. Our algorithms in this model lead to new bounds for some classic problems, and a "unified" algorithm whose performance matches previous results developed…
We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…
This report provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues,…
Stochastic parareal (SParareal) is a probabilistic variant of the popular parallel-in-time algorithm known as parareal. Similarly to parareal, it combines fine- and coarse-grained solutions to an ordinary differential equation (ODE) using a…
In this work, we present a novel algorithm design methodology that finds the optimal algorithm as a function of inequalities. Specifically, we restrict convergence analyses of algorithms to use a prespecified subset of inequalities, rather…
There are three main types of numerical computations for the Bessel function of the second kind: series expansion, continued fraction, and asymptotic expansion. In addition, they are combined in the appropriate domain for each. However,…
The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with…
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity…
The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and…
This work proposes a novel approach to evaluate and analyze the behavior of multi-population parallel genetic algorithms (PGAs) when running on a cluster of multi-core processors. In particular, we deeply study their numerical and…
Ordinal regression (OR) is classification of ordinal data in which the underlying categorical target variable has a natural ordinal relation for the underlying explanatory variable. For $K$-class OR tasks, threshold methods learn a…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
The past thirteen years have seen the development of many algorithms for approximating matrix functions in O(N) time, where N is the basis size. These O(N) algorithms rely on assumptions about the spatial locality of the matrix function;…