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- Zhongxiao Jia, Datian Niu
- SIAM J. Scientific Computing
- 2010

The harmonic Lanczos bidiagonalization method can be used to compute the smallest singular triplets of a large matrix A. We prove that for good enough projection subspaces harmonic Ritz values converge if the columns of A are strongly linearly independent. On the other hand, harmonic Ritz values may miss some desired singular values when the columns of A… (More)

- Zhongxiao Jia, Baochen Zhu
- Numerical Lin. Alg. with Applic.
- 2009

- Zhongxiao Jia, G. W. Stewart
- Math. Comput.
- 2001

This paper concerns the Rayleigh–Ritz method for computing an approximation to an eigenspace X of a general matrix A from a subspace W that contains an approximation to X. The method produces a pair (N, ˜ X) that purports to approximate a pair (L, X), where X is a basis for X and AX = XL. In this paper we consider the convergence of (N, ˜ X) as the sine of… (More)

- Zhongxiao Jia, Datian Niu
- SIAM J. Matrix Analysis Applications
- 2003

- Zhongxiao Jia
- Math. Comput.
- 2005

This paper concerns a harmonic projection method for computing an approximation to an eigenpair (λ, x) of a large matrix A. Given a target point τ and a subspace W that contains an approximation to x, the harmonic projection method returns an approximation (µ + τ, ˜ x) to (λ, x). Three convergence results are established as the deviation of x from W… (More)

- Zhongxiao Jia, Qian Zhang
- SIAM J. Scientific Computing
- 2013

We investigate the SPAI and PSAI preconditioning procedures and shed light on two important features of them: (i) For the large linear system Ax = b with A irregular sparse, i.e., with A having s relatively dense columns, SPAI may be very costly to implement, and the resulting sparse approximate inverses may be ineffective for preconditioning. PSAI can be… (More)

- Zhongxiao Jia, Yuquan Sun
- 2011

To implicitly restart the second-order Arnoldi (SOAR) method proposed by Bai and Su for the quadratic eigenvalue problem (QEP), it appears that the SOAR procedure must be replaced by a modified SOAR (MSOAR) one. However, implicit restarts fails to work provided that deflation takes place in the MSOAR procedure. In this paper, we first propose a Refined… (More)

- Zhongxiao Jia, Wenjie Kang
- Numerical Lin. Alg. with Applic.
- 2017

The SPAI algorithm, a sparse approximate inverse preconditioning technique for large sparse linear systems, proposed by Grote and Huckle [SIAM J. Sci. Com-put., 18 (1997), pp. 838–853.], is based on the F-norm minimization and computes a sparse approximate inverse M of a large sparse matrix A adaptively. However , SPAI may be costly to seek the most… (More)

- Zhongxiao Jia
- SIAM J. Matrix Analysis Applications
- 1995

- Zhongxiao Jia, Bingyu Li
- Numerische Mathematik
- 2013