Shutyaev, V. P.; Le Dimet, F.-X. Sensitivity of functionals of variational data assimilation problems. (English. Russian original) Zbl 1428.49045 Dokl. Math. 99, No. 3, 295-298 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 486, No. 4, 421-425 (2019). MSC: 49Q10 49K20 PDF BibTeX XML Cite \textit{V. P. Shutyaev} and \textit{F. X. Le Dimet}, Dokl. Math. 99, No. 3, 295--298 (2019; Zbl 1428.49045); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 486, No. 4, 421--425 (2019) Full Text: DOI
Shutyaev, Victor P. Adjoint equations in variational data assimilation problems. (English) Zbl 06866524 Russ. J. Numer. Anal. Math. Model. 33, No. 2, 137-147 (2018). MSC: 65K10 86A22 93B40 PDF BibTeX XML Cite \textit{V. P. Shutyaev}, Russ. J. Numer. Anal. Math. Model. 33, No. 2, 137--147 (2018; Zbl 06866524) Full Text: DOI
Gejadze, Igor Yu.; Shutyaev, Victor P.; Le Dimet, François-Xavier Hessian-based covariance approximations in variational data assimilation. (English) Zbl 1440.65061 Russ. J. Numer. Anal. Math. Model. 33, No. 1, 25-39 (2018). MSC: 65J22 65K10 PDF BibTeX XML Cite \textit{I. Yu. Gejadze} et al., Russ. J. Numer. Anal. Math. Model. 33, No. 1, 25--39 (2018; Zbl 1440.65061) Full Text: DOI
Shutyaev, Victor; Le Dimet, Francois-Xavier; Shubina, Elena Sensitivity with respect to observations in variational data assimilation. (English) Zbl 1365.65176 Russ. J. Numer. Anal. Math. Model. 32, No. 1, 61-71 (2017). MSC: 65K10 49J27 49M25 PDF BibTeX XML Cite \textit{V. Shutyaev} et al., Russ. J. Numer. Anal. Math. Model. 32, No. 1, 61--71 (2017; Zbl 1365.65176) Full Text: DOI
Brown, Kirsty L.; Gejadze, Igor; Ramage, Alison A multilevel approach for computing the limited-memory Hessian and its inverse in variational data assimilation. (English) Zbl 1348.65074 SIAM J. Sci. Comput. 38, No. 5, A2934-A2963 (2016). MSC: 65F30 65F08 15A09 65F15 PDF BibTeX XML Cite \textit{K. L. Brown} et al., SIAM J. Sci. Comput. 38, No. 5, A2934--A2963 (2016; Zbl 1348.65074) Full Text: DOI
Shutyaev, Victor; Vidard, Arthur; Le Dimet, François-Xavier; Gejadze, Igor On model error in variational data assimilation. (English) Zbl 1381.49043 Russ. J. Numer. Anal. Math. Model. 31, No. 2, 105-113 (2016). MSC: 49N90 49K15 65K10 65M32 PDF BibTeX XML Cite \textit{V. Shutyaev} et al., Russ. J. Numer. Anal. Math. Model. 31, No. 2, 105--113 (2016; Zbl 1381.49043) Full Text: DOI
Le Dimet, François-Xavier; Shutyaev, Victor; Parmuzin, Eugene Sensitivity of functionals with respect to observations in variational data assimilation. (English) Zbl 1335.86001 Russ. J. Numer. Anal. Math. Model. 31, No. 2, 81-91 (2016). MSC: 86-08 86A05 65K10 80A20 PDF BibTeX XML Cite \textit{F.-X. Le Dimet} et al., Russ. J. Numer. Anal. Math. Model. 31, No. 2, 81--91 (2016; Zbl 1335.86001) Full Text: DOI
Gejadze, I. Yu.; Shutyaev, V. On Gauss-verifiability of optimal solutions in variational data assimilation problems with nonlinear dynamics. (English) Zbl 1349.49037 J. Comput. Phys. 280, 439-456 (2015). MSC: 49M27 49N90 PDF BibTeX XML Cite \textit{I. Yu. Gejadze} and \textit{V. Shutyaev}, J. Comput. Phys. 280, 439--456 (2015; Zbl 1349.49037) Full Text: DOI
Rao, Vishwas; Sandu, Adrian A posteriori error estimates for the solution of variational inverse problems. (English) Zbl 1327.65135 SIAM/ASA J. Uncertain. Quantif. 3, 737-761 (2015). MSC: 65L09 65M32 PDF BibTeX XML Cite \textit{V. Rao} and \textit{A. Sandu}, SIAM/ASA J. Uncertain. Quantif. 3, 737--761 (2015; Zbl 1327.65135) Full Text: DOI arXiv
Cioaca, Alexandru; Sandu, Adrian Low-rank approximations for computing observation impact in 4D-Var data assimilation. (English) Zbl 1368.65015 Comput. Math. Appl. 67, No. 12, 2112-2126 (2014). MSC: 65C60 65K10 62P12 PDF BibTeX XML Cite \textit{A. Cioaca} and \textit{A. Sandu}, Comput. Math. Appl. 67, No. 12, 2112--2126 (2014; Zbl 1368.65015) Full Text: DOI
Cioaca, Alexandru; Sandu, Adrian; de Sturler, Eric Efficient methods for computing observation impact in 4D-Var data assimilation. (English) Zbl 1393.86018 Comput. Geosci. 17, No. 6, 975-990 (2013). MSC: 86A32 PDF BibTeX XML Cite \textit{A. Cioaca} et al., Comput. Geosci. 17, No. 6, 975--990 (2013; Zbl 1393.86018) Full Text: DOI
Bardsley, Johnathan M.; Parker, Albert; Solonen, Antti; Howard, Marylesa Krylov space approximate Kalman filtering. (English) Zbl 1289.65050 Numer. Linear Algebra Appl. 20, No. 2, 171-184 (2013). MSC: 65F10 93E11 90C20 86A05 86A10 PDF BibTeX XML Cite \textit{J. M. Bardsley} et al., Numer. Linear Algebra Appl. 20, No. 2, 171--184 (2013; Zbl 1289.65050) Full Text: DOI
Marchuk, G. I.; Shutyaev, V. P. Adjoint equations and iterative algorithms in problems of variational data assimilation. (English. Russian original) Zbl 1295.93031 Proc. Steklov Inst. Math. 276, Suppl. 1, S138-S152 (2012); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 17, No. 2, 136-150 (2011). MSC: 93B40 93B60 PDF BibTeX XML Cite \textit{G. I. Marchuk} and \textit{V. P. Shutyaev}, Proc. Steklov Inst. Math. 276, S138--S152 (2012; Zbl 1295.93031); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 17, No. 2, 136--150 (2011) Full Text: DOI
Gejadze, I. Yu.; Copeland, G. J. M.; Le Dimet, F.-X.; Shutyaev, V. Computation of the analysis error covariance in variational data assimilation problems with nonlinear dynamics. (English) Zbl 1408.65035 J. Comput. Phys. 230, No. 22, 7923-7943 (2011). MSC: 65J22 65M32 35Q53 PDF BibTeX XML Cite \textit{I. Yu. Gejadze} et al., J. Comput. Phys. 230, No. 22, 7923--7943 (2011; Zbl 1408.65035) Full Text: DOI
Auvinen, H.; Bardsley, J. M.; Haario, H.; Kauranne, T. The variational Kalman filter and an efficient implementation using limited memory BFGS. (English) Zbl 1197.65213 Int. J. Numer. Methods Fluids 64, No. 3, 314-335 (2010). MSC: 65Q10 65K05 90C06 90C30 90C53 39A50 PDF BibTeX XML Cite \textit{H. Auvinen} et al., Int. J. Numer. Methods Fluids 64, No. 3, 314--335 (2010; Zbl 1197.65213) Full Text: DOI
Gejadze, I. Yu.; Le Dimet, F.-X.; Shutyaev, V. On optimal solution error covariances in variational data assimilation problems. (English) Zbl 1185.65106 J. Comput. Phys. 229, No. 6, 2159-2178 (2010). MSC: 65K10 49J20 49M15 PDF BibTeX XML Cite \textit{I. Yu. Gejadze} et al., J. Comput. Phys. 229, No. 6, 2159--2178 (2010; Zbl 1185.65106) Full Text: DOI
Alekseev, A. K.; Navon, I. M. Criteria of optimality for sensors’ location based on adjoint transformation of observation data interpolation error. (English) Zbl 1196.80004 Int. J. Numer. Methods Fluids 62, No. 1, 74-89 (2010). Reviewer: Viktor Shevchuk (Lviv) MSC: 80A23 65M32 65M15 65N21 65N15 49K40 PDF BibTeX XML Cite \textit{A. K. Alekseev} and \textit{I. M. Navon}, Int. J. Numer. Methods Fluids 62, No. 1, 74--89 (2010; Zbl 1196.80004) Full Text: DOI