On the opodeictics of successive eigenvalue relaxation for large-scale eigenvalue problems: proofs of convergence estimates

Computing several eigenpairs of Hermitian problems by conjugate gradient iterations
Ovtchinnikov, E. 2008. Computing several eigenpairs of Hermitian problems by conjugate gradient iterations. Journal of Computational Physics. 227 (22), pp. 9477-9497. https://doi.org/10.1016/j.jcp.2008.06.038

Jacobi correction equation, line search, and conjugate gradients in Hermitian eigenvalue computation II: computing several extreme eigenvalues
Ovtchinnikov, E. 2008. Jacobi correction equation, line search, and conjugate gradients in Hermitian eigenvalue computation II: computing several extreme eigenvalues. SIAM Journal on Numerical Analysis. 46 (5), pp. 2593-2619. https://doi.org/10.1137/070688754

Jacobi correction equation, line search and conjugate gradients in Hermitian eigenvalue computation I: computing an extreme eigenvalue
Ovtchinnikov, E. 2008. Jacobi correction equation, line search and conjugate gradients in Hermitian eigenvalue computation I: computing an extreme eigenvalue. SIAM Journal on Numerical Analysis. 46 (5), pp. 2567-2592. https://doi.org/10.1137/070688742

Block locally optimal preconditioned eigenvalue Xolvers (BLOPEX) in Hypre and PETSc
Knyazev, A.V., Argentati, M.E., Lashuk, I. and Ovtchinnikov, E. 2007. Block locally optimal preconditioned eigenvalue Xolvers (BLOPEX) in Hypre and PETSc. SIAM Journal on Scientific Computing. 29 (5), pp. 2224-2239. https://doi.org/10.1137/060661624

Mathematical modelling and finite element simulation of smart tubular composites
Bondarev, P., Xanthis, L., Benjeddou, A. and Nasedkin, A. 2006. Mathematical modelling and finite element simulation of smart tubular composites. Computers & Structures. 84 (31-32), pp. 2385-2395. https://doi.org/10.1016/j.compstruc.2006.06.003

'Les fleurs du mal' II: a dynamically adaptive wavelet method of arbitrary lines for nonlinear evolutionary problems-capturing steep moving fronts
Ren, X. and Xanthis, L. 2006. 'Les fleurs du mal' II: a dynamically adaptive wavelet method of arbitrary lines for nonlinear evolutionary problems-capturing steep moving fronts. Computer Methods in Applied Mechanics and Engineering. 195 (37-40), pp. 4962-4970. https://doi.org/10.1016/j.cma.2005.10.022

Cluster robustness of preconditioned gradient subspace iteration eigensolvers
Ovtchinnikov, E. 2006. Cluster robustness of preconditioned gradient subspace iteration eigensolvers. Linear Algebra and its Applications. 415 (1), pp. 140-166. https://doi.org/10.1016/j.laa.2005.06.039

Cluster robust error estimates for the Rayleigh-Ritz approximation II: Estimates for eigenvalues
Ovtchinnikov, E. 2006. Cluster robust error estimates for the Rayleigh-Ritz approximation II: Estimates for eigenvalues. Linear Algebra and its Applications. 415 (1), pp. 188-209. https://doi.org/10.1016/j.laa.2005.06.041

Cluster robust error estimates for the Rayleigh-Ritz approximation I: Estimates for invariant subspaces
Ovtchinnikov, E. 2006. Cluster robust error estimates for the Rayleigh-Ritz approximation I: Estimates for invariant subspaces. Linear Algebra and its Applications. 415 (1), pp. 167-187. https://doi.org/10.1016/j.laa.2005.06.040

Sharp convergence estimates for the preconditioned steepest descent method for hermitian eigenvalue problems
Ovtchinnikov, E. 2006. Sharp convergence estimates for the preconditioned steepest descent method for hermitian eigenvalue problems. SIAM Journal on Numerical Analysis. 43 (6), pp. 2668-2689. https://doi.org/10.1137/040620643

A novel adaptive wavelet-based approach for a class of singularly perturbed partial differential equations
Bacopoulos, A., Konstantinou, V., Ren, X. and Xanthis, L. 2005. A novel adaptive wavelet-based approach for a class of singularly perturbed partial differential equations. HERMIS: the international journal of computer mathermatics and its applications. 5, pp. 1-6.

Asymptotic analysis of piezoelectric shallow shells
Sabu, N. and Xanthis, L. 2005. Asymptotic analysis of piezoelectric shallow shells. HERMIS: the International Journal of Computer Mathematics and its Applications. 5, pp. 91-108.

An effective wavelet method of arbitrary lines for problems with boundary and interior layers
Ren, X., Xanthis, L. and Konstantinou, V. 2004. An effective wavelet method of arbitrary lines for problems with boundary and interior layers. Proceedings of the International Conference on Boundary and Interior Layers (BAIL 2004). Toulouse, France 5-9 Jul 2004

'Les fleurs du mal': an adaptive wavelet method of arbitrary lines I: convection-diffusion problems
Ren, X. and Xanthis, L. 2004. 'Les fleurs du mal': an adaptive wavelet method of arbitrary lines I: convection-diffusion problems. Comptes Rendus Mecanique. 332 (1), pp. 23-29. https://doi.org/10.1016/j.crme.2003.10.004

'Les fleurs du mal': an adaptive wavelet-based method of arbitrary lines for problems with thin layers and moving fronts
Ren, X. and Xanthis, L. 2003. 'Les fleurs du mal': an adaptive wavelet-based method of arbitrary lines for problems with thin layers and moving fronts. HERMIS: the International Journal of Computer Mathematics and its Applications. 4.

Convergence estimates for the generalized davidson method for symmetric eigenvalue problems II: the subspace acceleration
Ovtchinnikov, E. 2003. Convergence estimates for the generalized davidson method for symmetric eigenvalue problems II: the subspace acceleration. SIAM Journal on Numerical Analysis. 41 (1), pp. 272-286. https://doi.org/10.1137/S0036142902411768

Convergence estimates for the generalized davidson method for symmetric eigenvalue problems I: the preconditioning aspect
Ovtchinnikov, E. 2003. Convergence estimates for the generalized davidson method for symmetric eigenvalue problems I: the preconditioning aspect. SIAM Journal on Numerical Analysis. 41 (1), pp. 258-271. https://doi.org/10.1137/S0036142902411756

On fast domain decomposition solving procedures for hp-discretizations of 3-d elliptic problems
Korneev, V.G., Langer, U. and Xanthis, L. 2003. On fast domain decomposition solving procedures for hp-discretizations of 3-d elliptic problems. Computational Methods in Applied Mathematics. 3 (4), pp. 536-559.

Solving finite element hp-discretizations of eliptic problems by fast domain decomposition algorithms
Xanthis, L. 2002. Solving finite element hp-discretizations of eliptic problems by fast domain decomposition algorithms. Trudy SpbGPU Prikladnaya Matematika (Transactions of St Petersburg State Polytechnic University, Applied Mathemetics). 485, pp. 126-153.

Symmetric spectral problems and asymptotically optimal algorithms: towards a harmony between the continuous and the discrete
D'Yakonov, E.G. and Xanthis, L. 2002. Symmetric spectral problems and asymptotically optimal algorithms: towards a harmony between the continuous and the discrete. HERMIS: the International Journal of Computer Mathematics and its Applications. 3, pp. 91-102.

Successive eigenvalue relaxation: a new method for the generalized eigenvalue problem and convergence estimates
Ovtchinnikov, E. and Xanthis, L. 2001. Successive eigenvalue relaxation: a new method for the generalized eigenvalue problem and convergence estimates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 457 (2006), pp. 441-451. https://doi.org/10.1098/rspa.2000.0674