A sequence of least squares problems of the form miny kG1=2(AT y h)k2, where G is an n n positive definite diagonal weight matrix, and A anm n (m n) sparse matrix with some dense columns; has many applications in linear programming, electrical networks, elliptic boundary value problems, and structural analysis. We suggest low-rank correction preconditioners for such problems, and a mixed solver...

We present and analyze a new iterative solver for implicit discretizations of simplified Boltzmann--Poisson system. The algorithm builds on recent work that incorporated sweeping ...

This article describes a fast direct solver (i.e., not iterative) for partial hierarchically semiseparable systems. This solver requires a storage of O(N logN) and has a computational complexity of O(N logN) arithmetic operations. The numerical benchmarks presented illustrate the method in the context of interpolation using radial basis functions. The key ingredients behind this fast solver are...

The boundary-element subregion-by-subregion (BE SBS) algorithm, developed in previous works, is employed to construct global block-diagonal preconditioners for BEM systems of equations. As the BE matrices for each BE subregion are independently assembled and stored, the block-diagonal-based preconditioners for the corresponding BE models are immediately constructed. A Krylov solver is embedded ...

This paper presents a combined adaptive finite element method with an iterative algebraic eigenvalue solver for a symmetric eigenvalue problem of asymptotic quasi-optimal computational complexity. The analysis is based on a direct approach for eigenvalue problems and allows the use of higher-order conforming finite element spaces with fixed polynomial degree. The asymptotic quasi-optimal adapti...

The paper presents the mathematical concepts underlying the new adaptive finite element code KASKADE, which, in its present form, applies to linear scalar second-order 2-D elliptic problems on general domains. Starting point for the new development is the recent work on hierarchical finite element bases due to Yserentant (1986). It is shown that this approach permits a flexible balance between ...

Frequency domain formulations of computational electromagnetic problems often require the solutions of complex-valued non-Hermitian systems of equations, which are still symmetric. For this kind of problems a whole class of sub-variant solver methods derived from the complex-valued Bi-Conjugate Gradient method is available. This class of methods contains established solution methods as the Conj...