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- Gene H. Golub, Peyman Milanfar, James M. Varah
- SIAM J. Scientific Computing
- 1999

We derive a stable technique, based upon matrix pencils, for the reconstruction of (or approximation by) polygonal shapes from moments. We point out that this problem can be considered the dual of 2â€¦ (More)

- David F. Gleich, Chen Greif, James M. Varah
- Numerical Lin. Alg. with Applic.
- 2013

Circulant matrices play a central role in a recently proposed formulation of three-way data computations. In this setting, a three-way table corresponds to a matrix where each â€˜scalarâ€™ is a vector ofâ€¦ (More)

- James M. Varah
- 2010

Extending some recent ideas of Butcher, we show how one can efficiently implement general implicit Runge-Kutta methods, including those based on Gaussian quadrature formulas which are particularlyâ€¦ (More)

- Gene H. Golub, Chen Greif, James M. Varah
- SIAM J. Matrix Analysis Applications
- 2005

We consider a positive definite block preconditioner for solving saddle point linear systems. An approach based on augmenting the (1,1) block while keeping its condition number small is described,â€¦ (More)

- Peyman Milanfar, Mihai Putinar, James M. Varah, Bj orn Gustafsson, Gene H. Golub
- 2000

In many areas of science and engineering, it is of interest to nd the shape of an object or region from indirect measurements. For instance, in geophysical prospecting, gravitational or magnetic eldâ€¦ (More)

- Chen Greif, James M. Varah
- SIAM J. Scientific Computing
- 1998

We consider the system of equations arising from finite difference discretization of a three-dimensional convection-diffusion model problem. This system is typically nonsymmetric. We show thatâ€¦ (More)

- Chen Greif, James M. Varah
- SIAM J. Matrix Analysis Applications
- 2006

We consider the problem of minimizing the condition number of a low rank modification of a matrix. Analytical results show that the minimum, which is not necessarily unique, can be obtained andâ€¦ (More)

- Chen Greif, James M. Varah
- SIAM J. Matrix Analysis Applications
- 2009

We offer a systematic study of Krylov subspace methods for solving skew-symmetric linear systems. For the method of conjugate gradients we derive a backward stable block decomposition ofâ€¦ (More)

We perform an algebraic analysis of a generalization of the augmented Lagrangian method for solution of saddle point linear systems. It is shown that in cases where the (1,1) block is singular,â€¦ (More)

- James M. Varah
- 2010

Introduction. In this paper, we are concerned with finding approximations to the eigenvectors of a general complex n X n matrix A, assuming good approximations to the eigenvalues have been found. Inâ€¦ (More)