### Abstract

Original language | English |
---|---|

Pages (from-to) | A2934-A2963 |

Number of pages | 30 |

Journal | SIAM Journal on Scientific Computing |

Volume | 38 |

Issue number | 5 |

DOIs | |

Publication status | Published - 28 Sep 2016 |

### Fingerprint

### Keywords

- data assimilation
- inverse Hessian
- limited memory
- preconditioning
- multigrid

### Cite this

}

*SIAM Journal on Scientific Computing*, vol. 38, no. 5, pp. A2934-A2963. https://doi.org/10.1137/15M1041407

**A multilevel approach for computing the limited-memory Hessian and its inverse in variational data assimilation.** / Brown, Kirsty L.; Gejadze, Igor; Ramage, Alison.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A multilevel approach for computing the limited-memory Hessian and its inverse in variational data assimilation

AU - Brown, Kirsty L.

AU - Gejadze, Igor

AU - Ramage, Alison

PY - 2016/9/28

Y1 - 2016/9/28

N2 - Use of data assimilation techniques is becoming increasingly common across many application areas. The inverse Hessian (and its square root) plays an important role in several different aspects of these processes. In geophysical and engineering applications, the Hessian-vector product is typically defined by sequential solution of a tangent linear and adjoint problem; for the inverse Hessian, however, no such definition is possible. Frequently, the requirement to work in a matrix-free environment means that compact representation schemes are employed. In this paper, we propose an enhanced approach based on a new algorithm for constructing a multilevel eigenvalue decomposition of a given operator, which results in a much more efficient compact representation of the inverse Hessian (and its square root). After introducing these multilevel approximations, we investigate their accuracy and demonstrate their efficiency (in terms of reducing memory requirements and/or computational time) using the example of preconditioning a Gauss-Newton minimisation procedure.

AB - Use of data assimilation techniques is becoming increasingly common across many application areas. The inverse Hessian (and its square root) plays an important role in several different aspects of these processes. In geophysical and engineering applications, the Hessian-vector product is typically defined by sequential solution of a tangent linear and adjoint problem; for the inverse Hessian, however, no such definition is possible. Frequently, the requirement to work in a matrix-free environment means that compact representation schemes are employed. In this paper, we propose an enhanced approach based on a new algorithm for constructing a multilevel eigenvalue decomposition of a given operator, which results in a much more efficient compact representation of the inverse Hessian (and its square root). After introducing these multilevel approximations, we investigate their accuracy and demonstrate their efficiency (in terms of reducing memory requirements and/or computational time) using the example of preconditioning a Gauss-Newton minimisation procedure.

KW - data assimilation

KW - inverse Hessian

KW - limited memory

KW - preconditioning

KW - multigrid

UR - https://www.siam.org/journals/sisc.php

U2 - 10.1137/15M1041407

DO - 10.1137/15M1041407

M3 - Article

VL - 38

SP - A2934-A2963

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

SN - 1064-8275

IS - 5

ER -