One-Stage Parallel Methods for the Numerical Solution of Ordinary Differential Equations
This paper studies one-stage block methods for solving the numerical solution of ordinary differential equations (ODES) in parallel, and a new family of one-stage methods is introduced. Each member in this family has a stability region equal to the ...
Two-Stage Parallel Methods for the Numerical Solution of Ordinary Differential Equations
This is a continuation of a previous work on finding parallel ODE methods with good stability regions. Based on the approach of zero-stable methods with perfect power stability polynomials, a family of two-stage block methods with stability regions ...
Simulation and Approximation of Stochastic Processes by Spline Functions
Error bounds for simultaneous approximation of stochastic processes by means of spline functions are derived. As opposed to conventional methods, conditions such as regularity of covariances, stationarity, continuity of sample paths, etc. can be dropped, ...
A Comparison of Three Mixed Methods for the Time-Dependent Maxwell’s Equations
Three mixed finite-element methods for approximating Maxwell’s equations are compared. A dispersion analysis provides a Courant–Friedrichs–Lewy (CFL) bound that is necessary for convergence when a uniform mesh is used. The dispersion analysis also allows ...
Adaptive Approximation by Piecewise Linear Polynomials on Triangulations of Subsets of Scattered Data
Given a set V of data points in $R^2 $ with corresponding data values, the problem of adaptive piecewise polynomial approximation is to choose a subset of points of V, to create a triangulation of this subset, and to define a piecewise linear surface over ...
The Modified Truncated SVD Method for Regularization in General Form
The truncated singular value decomposition (SVD) method is useful for solving the standard-form regularization problem: $\min ||{\bf x}||_2 $ subject to $\min ||A{\bf x} - {\bf b}||_2 $. This paper presents a modification of the truncated SVD method, ...
Highly Parallel Sparse Cholesky Factorization
This paper develops and compares several fine-grained parallel algorithms to compute the Cholesky factorization of a sparse matrix. The experimental implementations are on the Connection Machine, a distributed-memory SIMD machine whose programming model ...
Parallel Block-Partitioning of Truncated Newton for Nonlinear Network Optimization
Using the primal truncated Newton algorithm for the solution of nonlinear network optimization problems gives rise to very large and sparse systems of linear equations. These systems are solved iteratively with conjugate gradient methods. Using the ...
New Branch-and-Bound Rules for Linear Bilevel Programming
A new branch-and-bound algorithm for linear bilevel programming is proposed. Necessary optimality conditions expressed in terms of tightness of the follower’s constraints are used to fathom or simplify subproblems, branch and obtain penalties similar to ...
A Family of Block Preconditioners for Block Systems
The solution of block system $A_{mn} x = b$ by the preconditioned conjugate gradient method where $A_{mn} $ is an m-by-m block matrix with n-by-n Toeplitz blocks is studied. The preconditioner $c_F^{(1)} (A_{mn} )$ is a matrix that preserves the block ...
Efficient Solution of Parabolic Equations by Krylov Approximation Methods
This paper takes a new look at numerical techniques for solving parabolic equations by the method of lines. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of ...