# A new scheme of computing the approximate inverse preconditioner for the reduced linear systems

K. Moriya, T. Nodera

Research output: Contribution to journalArticle

5 Citations (Scopus)

### Abstract

In this paper, we propose a new implementation of the Newton scheme of an approximate preconditioner for the reduced linear system. In the original Newton scheme, the trouble is that the computation cost of the matrix-matrix product is always so expensive. On the other hand, the proposed implementation computes the preconditioner implicitly and reduces the cost of constructing the preconditioner by using the matrix-vector product form. We also show that the proposed implementation is less expensive than computing the preconditioner in explicit form.

Original language English 345-352 8 Journal of Computational and Applied Mathematics 199 2 https://doi.org/10.1016/j.cam.2005.08.033 Published - 2007 Feb 15

### Fingerprint

Approximate Inverse
Preconditioner
Linear systems
Linear Systems
Computing
Matrix Product
Product Form
Cross product
Costs

### Keywords

• Greedy algorithm
• Newton scheme
• Preconditioner
• Reduced linear system
• Schur complement

### ASJC Scopus subject areas

• Applied Mathematics
• Computational Mathematics
• Numerical Analysis

### Cite this

A new scheme of computing the approximate inverse preconditioner for the reduced linear systems. / Moriya, K.; Nodera, T.

In: Journal of Computational and Applied Mathematics, Vol. 199, No. 2, 15.02.2007, p. 345-352.

Research output: Contribution to journalArticle

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