Fortran linear inverse problem solver

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August 2010, 4(3): 485-503. doi: 10.3934/ipi.2010.4.485

Fortran linear inverse problem solver

Mikko Orispää ^1, and Markku Lehtinen ^2,

1.	Sodankylä Geophysical Observatory, University of Oulu, Tähteläntie 62, FIN-99600 Sodankylä
2.	University of Oulu, Sodankylä Geophysical Observatory, Sodankylä

Received December 2008 Revised January 2010 Published July 2010

Abstract
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FLIPS (Fortran Linear Inverse Problem Solver) is a Fortran 95 module for solving large-scale statistical linear systems. Instead of inverting large matrices, FLIPS transforms the system into a simpler one by using Givens rotations. This simplified system is then solved by FLIPS quickly and efficiently. FLIPS is also capable of calculating the full a posteriori covariance matrix. It is also possible to add or delete measurements and unknowns making it useful in time-dependent problems of the Kalman-filter type. The FLIPS implementation is explained and the advantages of using FLIPS, especially for overdetermined systems, are shown. Plans for future developments are discussed.

Keywords: linear solver, Statistical inverse problems, Givens rotations., matrix inverse.

Mathematics Subject Classification: Primary: 68-04, Secondary: 65F05, 93E2.

Citation: Mikko Orispää, Markku Lehtinen. Fortran linear inverse problem solver. Inverse Problems & Imaging, 2010, 4 (3) : 485-503. doi: 10.3934/ipi.2010.4.485

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