A real algorithm for the Hermitian eigenvalue decomposition

Modifying complex plane rotations, we derive a new Jacobi-type algorithm for the Hermitian eigendecomposition, which uses only real arithmetic. When the fast-scaled rotations are incorporated, the new algorithm brings a substantial reduction in computational costs. The new method has the same convergence properties and parallelism as the symmetric Jacobi algorithm. Computational test results show that it produces accurate eigenvalues and eigenvectors and achieves great reduction in computational time.The work of this author was supported in part by the National Science Foundation grant CCR-8813493 and by the University of Minnesota Army High Performance Computing Research Center contract DAAL 03-89-C-0038.The work of this author was supported in part by the University of Minnesota Army High Performance Computing Research Center contract DAAL 03-89-C-0038.     

Modelling of composting of food waste in a column reactor

The composting of organic solid waste, the mixture of fruit and vegetable leftovers enriched with night soil, was investigated in a closed thermally insulated reactor. It was found that 80.9 % of the original substrate biodegraded after 14 days. A mathematical model of the column reactor was proposed where the biodegradation rate of the organic solid waste was described using simple n-thorder kinetics. A good prediction of process performance was obtained using the proposed kinetics and experimentally obtained reaction heat. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Reaction and mass transfer effects in a catalytic monolith reactor

Zeolite-based monoliths (Cu/ZSM-5 on cordierite) are prepared and used to catalyze direct decomposition of nitrogen monoxide. Two-dimensional heterogeneous model is applied to describe the behavior of the monolith reactor, with the emphasis on the features introduced due to coupling of flow, mass transfer and chemical reaction. The proposed model has been verified by comparing computer simulation data with laboratory experimental data. It is shown that both inter- and intraphase diffusion limitations have to be considered when modeling complex reactor configuration, such as monolith reactors, especially when monolith with thicker catalytic layer are used at higher temperatures.     

Kinetics of no decomposition over Cu/ZSM-5 catalyst

The kinetics of catalytic decomposition of NO over Cu/ZSM-5 catalyst has been studied in an integral flow reactor at atmospheric pressure. Kinetic analysis is based on the assumption that the surface reaction represents the rate-determining step. On the basis of theoretical considerations of different interactions between reactants and catalyst, and experimental evidences, three different mechanistic kinetic models were chosen. Also a power-law model was tested. The best agreement has been achieved with the model

On the cubic convergence of the Paardekooper method

We show a simple way how asymptotic convergence results can be conveyed from a simple Jacobi method to a block Jacobi method. Our pilot methods are the well known symmetric Jacobi method and the Paardekooper method for reducing a skew-symmetric matrix to the real Schur form. We show resemblance in the quadratic and cubic convergence estimates, but also discrepances in the asymptotic assumptions. By numerical tests we confirm that our asymptotic assumptions for the Paardekooper method are most general.     

On quadratic convergence bounds for theJ-symmetric Jacobi method

Summary This paper deals with quadratic convergence estimates for the serialJ-symmetric Jacobi method recently proposed by Veseli. The method is characterized by the use of orthogonal and hyperbolic plane rotations. Using a new technique recently introduced by Hari we prove sharp quadratic convergence bounds in the general case of multiple eigenvalues.     

On the global and cubic convergence of a quasi-cyclic Jacobi method

Summary In this paper we consider the global and the cubic convergence of a quasi-cyclic Jacobi method for the symmetric eigenvalue, problem. The method belongs to a class of quasi-cyclic methods recently proposed by W. Mascarenhas. Mascarenhas showed that the methods from his class asymptotically converge cubically per quasi-sweep (one quasi-sweep is equivalent to 1.25 cyclic sweeps) provided the eigenvalues are simple. Here we prove the global convergence of our method and derive very sharp asymptotic convergence bounds in the general case of multiple eigenvalues. We discuss the ultimate cubic convergence of the method and present several numerical examples which all well comply with the theory.This work was supported in part by the University of Minnesota Army High Performance Computing Research Center and the U.S Army Contract DAAL03-89-C-0038. The paper was partly written while this author was a visiting faculty in the Department of Mathematics, University of Kansas, Lawrence, Kansas. The first version of this paper was made in July 1990 while this author was visiting AHPCRC.     

Crosslinking of an unsaturated polyester resin in the mould: Modelling and heat transfer studies

The crosslinking of unsaturated polyester was studied by using an experiment and a mathematical model of the process. Temperature–time profiles were recorded in the centre of the sample inside the mould at the outer wall of the cylindrical copper mould, and in the bulk of the heated air bath. A numerical model was constructed by taking into account the heat transferred by convection from the air to the mould surface and the heat transferred by conduction through the resin, as well as the heat generated by the crosslinking reaction. The convection heat transfer coefficient was determined in independent experiments with the empty copper mould. Introduction of the carbon base filler reduced the amount of heat generated in the composite due to the less reactive component in the composite. As a result, it lowered the temperature of the resin. By recording the temperature-time and the degree of crosslinking time profiles developed within the sample extensive knowledge of the process can be obtained. The effects of the convection heat transfer on the rate of mould heating, and the conduction heat transfer through the mould as well as the internal heat generated by the crosslinking reaction are visibly shown, despite a complexity of the process.     

Globally convergent Jacobi methods for positive definite matrix pairs

The paper derives and investigates the Jacobi methods for the generalized eigenvalue problem A x = λ B x, where A is a symmetric and B is a symmetric positive definite matrix. The methods first “normalize” B to have the unit diagonal and then maintain that property during the iterative process. The global convergence is proved for all such methods. That result is obtained for the large class of generalized serial strategies from Hari and Begovi? Kova? (Trans. Numer. Anal. (ETNA) 47, 107–147, 2017). Preliminary numerical tests confirm a high relative accuracy of some of those methods, provided that both matrices are positive definite and the spectral condition numbers of Δ _A AΔ _A and Δ _B BΔ _B are small, for some nonsingular diagonal matrices Δ _A and Δ _B .