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- Ren-Cang Li
- SIAM J. Matrix Analysis Applications
- 1998

The classical perturbation theory for Hermitian matrix eigenvalue and singular value problems provides bounds on invariant subspace variations that are proportional to the reciprocals of absoluteâ€¦ (More)

- Wei-guo Wang, Wei-chao Wang, Ren-Cang Li
- SIAM J. Matrix Analysis Applications
- 2012

A new doubling algorithmâ€”the alternating-directional doubling algorithm (ADDA)â€” is developed for computing the unique minimal nonnegative solution of an M -matrix algebraic Riccati equation (MARE).â€¦ (More)

- Peter Benner, Ren-Cang Li, Ninoslav Truhar
- J. Computational Applied Mathematics
- 2009

This paper is concerned with the numerical solution of large scale Sylvester equations AX âˆ’XB = C, Lyapunov equations as a special case in particular included, with C having very small rank. Forâ€¦ (More)

- Nicholas J. Higham, Ren-Cang Li, FranÃ§oise Tisseur
- SIAM J. Matrix Analysis Applications
- 2007

The most widely used approach for solving the polynomial eigenvalue problem P (Î»)x = (âˆ‘m i=0 Î» Ai ) x = 0 in n Ã— n matrices Ai is to linearize to produce a larger order pencil L(Î») = Î»X + Y , whoseâ€¦ (More)

- Ren-Cang Li
- 2005

Conjugate Gradient (CG) method is often used to solve a positive definite linear system Ax = b. Existing bounds suggest that the residual of the kth approximate solution by CG goes to zero like [( âˆšâ€¦ (More)

- Ren-Cang Li, Qiang Ye
- SIAM J. Matrix Analysis Applications
- 2003

We present a Krylov subspaceâ€“type projection method for a quadratic matrix polynomial Î»2I âˆ’ Î»A âˆ’ B that works directly with A and B without going through any linearization. We discuss a special caseâ€¦ (More)

- Ren-Cang Li
- 1996

The classical perturbation theory for Hermitian matrix eigenvalue and singular value problems provides bounds on the absolute differences between approximate eigenvalues (singular values) and theâ€¦ (More)

- William Kahan, Ren-Cang Li
- Math. Comput.
- 1997

Many models of physical and chemical processes give rise to ordinary differential equations with special structural properties that go unexploited by general-purpose software designed to solveâ€¦ (More)

- Zhaojun Bai, Ren-Cang Li
- SIAM J. Matrix Analysis Applications
- 2013

In Part I of this paper we presented a minimization principle and related theoretical results for the linear response eigenvalue problem. Here we develop best approximations of the smallest fewâ€¦ (More)

- Jungong Xue, Shufang Xu, Ren-Cang Li
- Numerische Mathematik
- 2012

This paper is concerned with the relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Algebraic Riccati Equations (MARE) XDX âˆ’AX âˆ’XB + C = 0 by whichâ€¦ (More)