SIAM Journal on Scientific and Statistical Computing

Several remarkable theoretical and computational properties of reacting shock waves are both documented and analyzed. In particular, for sufficiently small heat release or large reaction rate, we demonstrate that the reacting compressible Navier–Stokes ...

We introduce a new multigrid continuation method for computing solutions of nonlinear elliptic eigenvalue problems which contain limit points (also called turning points or folds). Our method combines the frozen tau technique of Brandt with pseudo-arc ...

We consider a family of finite element spaces and minimize an energy functional over each space. The space which allows the lowest energy is considered “optimal.” Such a family is constructed by starting with an initial “triangulation” and refining one ...

We describe a new parallel algorithm for computing the CS-decomposition, and compare it against a recently published method of Kaplan and Van Loan. For a $2n \times n$ orthonormal matrix that is partitioned into two square blocks, their procedure needs $...

An algorithm is described for computing the generalized singular value decomposition of $A(m \times n)$ and $B(p \times n)$. Unitary matrices U, V and Q are developed so that $U^H AQ$ and $V^H BQ$ have as many nonzero parallel rows as possible, and ...

An algorithm is developed for computing the singular value decomposition of a product of two general matrices without explicitly forming the product. The algorithm is based on an earlier Jacobi-like method due to Kogbetliantz and uses plane rotations ...

A quadratically convergent Newton method for computing the polar decomposition of a full-rank matrix is presented and analysed. Acceleration parameters are introduced so as to enhance the initial rate of convergence and it is shown how reliable ...

The stability of the computational process in the solution of systems of linear algebraic equations $Ax = b$ depends on the condition number of matrix A. Reliable and efficient algorithms for calculating estimates of the condition number of a matrix are ...

This paper introduces general row merging schemes for the $QR$ decomposition of sparse matrices by Givens rotations. They can be viewed as a generalization of row rotations to submatrix rotations (or merging) in the recent method by George and Heath [12]...

The profile reduction method is intended for time and storage reduction in solving a linear system of equations $Mx = b$ using direct methods.A Frontal Increase Minimization strategy (FIM strategy) is a generalization of the so-called King's numbering ...

Two fourth order accurate approximations to general linear fourth order two-point boundary value problems with Dirichlet boundary conditions are evaluated. The first is a new implementation of the operator compact implicit (OCI) method. Its derivation ...

This paper investigates the absolute stability properties of numerical methods for initial value O.D.E.'s based on second derivative formulae where the regular iteration matrix, which is of the form $(I - \beta _0 hJ - \gamma _0 h^2 J^2 )$, is ...

We describe numerical methods for the detection of multiple bifurcations on solution paths of certain gradient maps, and for effecting the branching off via appropriate local perturbations. Our model problems are quasi-linear elliptic boundary value ...

In most physical problems, there are conservation laws which take the form of integral identities. Some of these are “flow balance” conditions across interfaces. In the process of discretization, some or all of the integral identities may be lost, ...

We present a method for the linear inversion (deconvolution) of band-limited reflection seismograms. A large convolution problem is first broken up into a sequence of smaller problems. Each small problem is then posed as an optimization problem to ...

In this paper we analyze error propagation in layer-peeling inversion methods. A bound for the error in recovering the reflection coefficient at a certain depth is given in terms of the estimated reflection coefficients. The error propagation results ...

The Random Choice Method for single scalar conservation laws is examined, and an approximate Riemann solver is constructed. The construction is accomplished using a result of Dafermos regarding the solution of a single conservation law with a general ...

A probabilistic method is presented to solve reaction diffusion equations. A random walk is combined with creation and destruction of elements. The method is applied to Nagumo's equation. Numerical results are given demonstrating convergence of the ...

A system of diffusion equations modeling free convection near a wall is solved by a grid free random walk method that involves creation of the vorticity at the boundary. We prove that the pointwise error and the least squares error of the computed ...

It is shown that the effect of cancellation errors in a quasi-Newton method can be predicted with reasonable accuracy on the basis of simple formulae derived by using probabilistic arguments. Errors induced by cancellation are shown to have the ...

Two p-variate normal populations $N_p ({\bf {\mu}} _1 ,\Sigma _1 )$, $N_p ({\bf {\mu}} _2 ,\Sigma _2 )$ with parameters known and ${\bf {\mu}} _1 \ne {\bf {\mu}} _2 $, $\Sigma _1 \ne \Sigma _2 $ are considered. A method is given to calculate, to a ...