Numerical analysis as a separate research topic in mathematics started in the early years (1940-1950) of the arrival of electronic computers. It is concerned with the efficient numerical solution of problems derived from mathematical models. As these models describe many aspects of the world, predictive quantitative information will be obtained from the numerical solutions of the problems. Since many years numerical analysis is a well established discipline at most universities and research laboratories.
In general one studies algorithms for the determination of numerical approximate values for the solution of mathematical problems (like partial differential equations, large systems of linear equations and non-linear equations) with full error control. Furthermore one develops efficient methods to provide solutions with the help of (parallel) computers.
Typical problems are stated frequently in the form of partial differential equations or as systems of linear equations with a large number of unknowns. Numerical Linear Algebra is concerned with the stability of the solutions with respect to perturbation of data and with the development of algorithms to compute the solutions and their computational complexity.
Among my research interests in the area are:
  • Multigrid methods for generalized Stokes equations
  • Algebraic Multilevel Iteration Methods
  • Iterative Preconditioned Methods
  • Multigrid Eigensolvers
  • Parallel algorithms
  • Direct Methods


Scientific interests




M. Larin; A. Reusken, A comparative study of efficient iterative solvers for generalized Stokes equations,
Numerical Linear Algebra with Applications, 15 (2008), pp.13-34.
M. Larin;, On a modification of algebraic multilevel iteration method for finite element matrices,
Sib. J. Num. Math., 10 (2007), pp.61-76.
M. Larin; V.P. Il'in, Variable-step preconditioned conjugate gradient method for partial symmetric eigenvalue problems,
Russ. J. Numer. Anal. Math. Modelling, 20 (2005), pp. 161-184.
M. Larin, Using a compensation principle in algebraic multilevel iteration method for finite element matrices,
Sib. J. Num. Math., 8 (2005), pp.127-142.
M. Larin, A. Padiy, On the theory of the generalized augmented matrix preconditioning method,
Sib. J. Num. Math., 7 (2004), pp.335-343.
M. Larin, On a multigrid method for solving partial eigenproblems,
Sib. J. Num. Math., 7 (2004), pp.25-42.
O. Axelsson, M. Larin, An element-by-element version of variable-step multilevel preconditioning methods,
Sib. J. Num. Math., 6 (2003), pp. 209-226.
M. Larin, On a multigrid eigensolver for linear elasticity problems,
Lect. Notes in Computer Science, 2542 (2003), pp. 182-191.
M. Larin, Computation of a few smallest eigenvalues and their eigenvectors for large sparse SPD matrices,
Bull. Nov. Compt. Center, Num. Anal., 11 (2002), pp. 75-86.
G. Pasquinelli, C.-A. Thole., M. Larin, Introduction of parallelization techniques into the FEM code NOSA for the dynamic structural analysis of historical buildings,
Proceeeding of CRN-GMD Workshop, Berlin, Germany, 9-10 March, 2000, CNR-CNUCE, Pisa, May 2000, pp. 21-25.
M. Larin, An optimal multilevel method for computing the smallest eigenpair,
Bull. Nov. Compt. Center, Num. Anal., 9 (2000), pp. 59-67.
M. Larin, An optimal incomplete factorization method for Stieltjes matrices,
in Recent advances in numerical methods and applications, (O. Iliev, M. Kaschiev, S. Margenov, B. Sendov, P. Vassilevski,eds.), World Scientific Publ. Co., Singapur, 1999, pp. 696-704.
M. Larin, An algebraic multilevel iterative method of incomplete factorization for Stieltjes matrices,
Comput. Math. Math. Physics, 38 (1998), pp. 1011-1025.
M. Larin, On the theory of algebraic multilevel iteration methods for Stieltjes matrices,
Bull. Nov. Compt. Center, Num. Anal., 8 (1998), pp. 57-70.
O. Axelsson, M. Larin, An algebraic multilevel iteration method for finite element matrices,
J. Comput. Appl. Mathematics, 89 (1997), pp. 135-153.
M. Larin, An iterative multilevel incomplete factorization method for solving five-point system of equations,
Bull. Nov. Compt. Center, Num. Anal., 5 (1996), pp. 69-88.
M. Larin, A.V. Shirin, Parallel variant of cross-methods for solving grid system of equations,
Bull. Nov. Compt. Center, Num. Anal., 3 (1995), pp. 74-92.
M. Larin, Quadri-storage scheme for sparse Cholesky factor and tree-based implementation of Cholesky method,
in Advanced Mathematics, Computations and Applications, (A.S.Alekseev, N.S.Bakhvalov, eds.), Novosibirsk, 1995, pp. 428-434.
V.P. Il'in, V.I. Karnachuk, M. Larin, Tree-based approach to data structure for Cholesky factorization,
Comput. Math. Math. Physics, 34 (1994), pp. 1503-1510.
V.P. Il'in, M.  Larin, One iterative method of solving finite difference Helmgoltz equation on sphere,
Russ. J. Numer. Anal. Math. Modelling, 8 (1993), pp. 297-309.