Factorized-Sparse-Approximate-Inverse Preconditionings of Linear Systems with Unsymmetric Matrices

The paper considers the application of factorized-sparse-approximate-inverse (FSAI) preconditionings to linear algebraic systems with nonsingular unsymmetric coefficient matrices. Special attention is paid to methods for optimizing the sparsity pattern of such preconditioners. It is numerically demonstrated that the efficiency of FSAI preconditionings can be substantially improved by applying the so-called postfiltering and prefiltering in order to sparsify preconditioning matrices. Bibliography: 20 titles.     

Prefiltration technique via aggregation for constructing low‐density high‐quality factorized sparse approximate inverse preconditionings

This paper considers a new approach to a priori sparsification of the sparsity pattern of the factorized approximate inverses (FSAI) preconditioner using the so‐called vector aggregation technique. The suggested approach consists in construction of the FSAI preconditioner to the aggregated matrix with a prescribed sparsity pattern. Then small entries of the computed ‘aggregated’ FSAI preconditioning matrix are dropped, and the resulting pointwise sparsity pattern is used to construct the low‐density block sparsity pattern of the FSAI preconditioning matrix to the original matrix. This approach allows to minimize (sometimes significantly) the construction costs of low‐density high‐quality FSAI preconditioners. Numerical results with sample matrices from structural mechanics and thin shell problems are presented. Copyright © 2002 John Wiley & Sons, Ltd.     

An Automatic Procedure for Updating the Block Size in the Block Conjugate Gradient Method for Solving Linear Systems

The paper considers the problem of constructing an efficient automatic procedure for reducing the block size in the block conjugate gradient method insuring that the resulting rate of convergence is comparable with that of the block conjugate gradient method with constant block size. The numerical results provided show that, independently of the type of distribution of the smallest eigenvalues of the preconditioned matrix, the procedure suggested always leads to a decrease of the arithmetic costs with respect to those of the block method with constant block size. Bibliography: 8 titles.     

Electrochemical co-oxidation of C-H acids and methanol as a new route to functionalized cyclopropanes

Electrolysis of dimethyl malonate or methyl cyanoacetate in methanol in the presence of LiCl in an undivided cell leads to formation of 1,1,2,2-cyclopropanetetracarboxylic derivatives.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1835–1836, October, 1994.This work was supported by the International Science Foundation (Grant No MHY 000).     

Solid-phase oxidative halodecarboxylation of β-arylacrylic acids with the ceric ammonium nitrate—alkali halide system

The solid-phase oxidation of cinnamic, 4-methoxy- and 3,4-dimethoxycinnamic acids with Ce(NH₄)₂(NO₃)₆—MHal system leads to β-halostyrenes. Similar procedure in the absence of a metal halide results in a cleavage of the C=C bond giving the corresponding benzaldehydes. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 114–118, January, 2008.     

Stereoselective electrocatalytic cyclization of 3-substituted 2,2-dicyanocyclopropane-1,1-dicarboxylic acid esters to form 6-substituted (1R,5R,6R)*-4,4-dialkoxy-5-cyano-2-oxo-3-azabicyclo[3.1.0]hexane-1-carboxylic acid esters

Electrolysis of 3-substituted 2,2-dicyanocyclopropane-1,1-dicarboxylic acid esters in alcohols in an undivided cell in the presence of NaBr or NaOAc afforded 6-substituted (1R,5R, 6R)*-4,4-dialkoxy-5-cyano-2-oxo-3-azabicyclo[3.1.0]hexane-1-carboxylic acid esters in 80–95% yields. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 102–107, January, 2006.     

Kinetics of the alkylation of butyraldehyde by 1-heptene in acetic acid by the action of Mn(III) acetate

Conclusions The kinetics of the reaction of the butyraldehyde with 1-heptene in acetic acid by the action of Mn(III) acetate (in an inert atmosphere) supports the previously proposed mechanism for the catalytic alkylation of aldehydes by olefins. In accord with this mechanism, the selectivity in the formation of -alkyl-substituted aldehydes is attributed to the reaction proceeding in the coordination sphere of the metal.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 2, pp. 384–388, February, 1984.     

Ring expansion of 4,4-diethyl-1,2-dithiolane in the reaction with butylacetylene. Involvement of anion and radical intermediates

The action of lithium butyl acetylenide in THF causes 4,4-diethyl-1,2-dithiolane to undergo ring-opening to form 2,2-diethyl-4-thia-5-decyne-1-thiol, which cyclizes to give 2-butyl-6,6-diethyl-5,6-dihydro-1,4-dithiepin by either a homolytic or a nucleophilic mechanism. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 204–206, January, 1997.