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- Jianlin Xia, Yuanzhe Xi, Ming Gu
- SIAM J. Matrix Analysis Applications
- 2012

We propose a superfast solver for Toeplitz linear systems based on rank structured matrix methods and randomized sampling. The solver uses displacement equations to transform a Toeplitz matrix T intoâ€¦ (More)

- Yuanzhe Xi, Jianlin Xia, Raymond H. Chan
- SIAM J. Matrix Analysis Applications
- 2014

In this paper, we propose a structured bisection method with adaptive randomized sampling for finding selected or all of the eigenvalues of certain real symmetric matrices A. For A with a low-rankâ€¦ (More)

- Yuanzhe Xi, Jianlin Xia, Stephen Cauley, Venkataramanan Balakrishnan
- SIAM J. Matrix Analysis Applications
- 2014

We present some superfast (O((m + n) log(m + n)) complexity) and stable structured direct solvers for mÃ— n Toeplitz least squares problems. Based on the displacement equation, a Toeplitz matrix T isâ€¦ (More)

- Yuanzhe Xi, Yousef Saad
- SIAM J. Scientific Computing
- 2016

We present a method for computing partial spectra of Hermitian matrices, based on a combination of subspace iteration with rational filtering. In contrast with classical rational filters derived fromâ€¦ (More)

- Ruipeng Li, Yuanzhe Xi, Eugene Vecharynski, Chao Yang, Yousef Saad
- SIAM J. Scientific Computing
- 2016

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in theâ€¦ (More)

- Jianlin Xia, Yuanzhe Xi, Stephen Cauley, Venkataramanan Balakrishnan
- SIAM J. Matrix Analysis Applications
- 2015

We propose a fast structured selected inversion method for extracting the diagonal blocks of the inverse of a sparse symmetric matrix A, using the multifrontal method and rank structures. When Aâ€¦ (More)

- Yuanzhe Xi, Jianlin Xia
- SIAM J. Matrix Analysis Applications
- 2016

In this paper, we investigate the numerical error propagation and provide systematic backward stability analysis for some hierarchical rank structured matrix algorithms. We prove the backwardâ€¦ (More)

- Yuanzhe Xi, Yousef Saad
- SIAM J. Scientific Computing
- 2017

This paper introduces a rational function preconditioner for linear systems with indefinite sparse matrices A. By resorting to rational functions of A, the algorithm decomposes the spectrum of A intoâ€¦ (More)

- Yuanzhe Xi, Yousef Saad
- 2015

This paper presents a method for computing partial spectra of Hermitian matrices, based on a subspace iteration method combined with rational filtering. While the general approach is the same as thatâ€¦ (More)

- D. Cai, Edmond Chow, Lucas Erlandson, Yousef Saad, Yuanzhe Xi
- Numerical Lin. Alg. with Applic.
- 2018

This paper presents an efficient method to perform Structured Matrix Approximation by Separation and Hierarchy (SMASH), when the original dense matrix is associated with a kernel function. Givenâ€¦ (More)