Householder method

Banachiewicz method, 67 characteristic roots, 67 characteristic vectors, 67 Cholesky method, 67 Danilevskii method, 74 deflation, 71 derogatory form, 73 "equations of motion, 418 Givens method, 75 Hessenberg form, 73 Hessenberg method, 75 Householder method, 75 Jacobi method, 71 Krylov method, 73 Lanczos form, 78 method of modification, 67 method of relaxation, 62 method of successive displacements,... 

In fact, the Lanczos reduction was originally proposed as a tridiagonalization scheme, predating the Givens and Householder methods. Unlike the latter methods, however, the Lanczos method is recursive. This means that the dimensionality of the T matrix is determined by the number of steps of the Lanczos recursion (K), which is usually much smaller than the dimensionality of the Hamiltonian matrix (N) in real calculations. 

Like the Broyden-Householder method, Kubicek algorithm is based on Householder s identity.19... 

Transform a whole row (and column) to zero in one step which is not regenerated by subsequent transformations the Householder method... 

The Givens and Householder methods are both proportional to in their time consumption. 

The method which has been implemented to generate the eigenvalues and eigenvectors of a real symmetric matrix is not, in fact, the fastest method there are methods which have asymptotic dependence on floating point operations, while the Jacobi method depends asymptotically on m. f77 implementations of these methods (the Givens and Householder methods) are available for most computers and calls to eigen may be simply replaced by corresponding calls to the other routine. 

A household method for treating the common cold is to take tablets of vitamin C or food that is rich in this vitamin (rosehip tea, lemon). Does this practice withstand scientific scratiny ... 

METHOD 2 By far the most popular method currently available. This is a really convenient way to convert P2P or MD-P2P into meth and MDMA ( ecstacy ). It is a very clean procedure, akin to that of the NaBHgCN method, using amalgamated aluminum catalyst made from ordinary household foil [26, 28]. When Strike was reading all the underground literature on the use of household... 

It would be difficult to over-estimate the extent to which the BET method has contributed to the development of those branches of physical chemistry such as heterogeneous catalysis, adsorption or particle size estimation, which involve finely divided or porous solids in all of these fields the BET surface area is a household phrase. But it is perhaps the very breadth of its scope which has led to a somewhat uncritical application of the method as a kind of infallible yardstick, and to a lack of appreciation of the nature of its basic assumptions or of the circumstances under which it may, or may not, be expected to yield a reliable result. This is particularly true of those solids which contain very fine pores and give rise to Langmuir-type isotherms, for the BET procedure may then give quite erroneous values for the surface area. If the pores are rather larger—tens to hundreds of Angstroms in width—the pore size distribution may be calculated from the adsorption isotherm of a vapour with the aid of the Kelvin equation, and within recent years a number of detailed procedures for carrying out the calculation have been put forward but all too often the limitations on the validity of the results, and the difficulty of interpretation in terms of the actual solid, tend to be insufficiently stressed or even entirely overlooked. And in the time-honoured method for the estimation of surface area from measurements of adsorption from solution, the complications introduced by... 

Aerosols can be produced as a spray of droplets by various means. A good example of a nebulizer is the common household hair spray, which produces fine droplets of a solution of hair lacquer by using a gas to blow the lacquer solution through a fine nozzle so that it emerges as a spray of small droplets. In use, the droplets strike the hair and settle, and the solvent evaporates to leave behind the nonvolatile lacquer. For mass spectrometry, a spray of a solution of analyte can be produced similarly or by a wide variety of other methods, many of which are discussed here. Chapters 8 ( Electrospray Ionization ) and 11 ( Thermospray and Plasmaspray Interfaces ) also contain details of droplet evaporation and formation of ions that are relevant to the discussion in this chapter. Aerosols are also produced by laser ablation for more information on this topic, see Chapters 17 and 18. 

A Hessenberg form H (the same form but not the same matrix) can also be obtained by a sequence of orthogonal transformations, either by plane rotations (the method of Givens), each rotation annihilating an individual element, or by using unitary hermitians, I — 2wiwf, wfwt = 1 (the method of Householder), each of which annihilates ill possible elements in a column. Thus, at the first step, if A = A, and... 

Thiophenes of type 31 (X-Y = CH) were generated via Lawesson s reagent-mediated cyclization of 1,4-dicarbonyl compounds 30 under microwave irradiation in the absence of solvent [37]. The reaction was carried by mixing the two solid reagents in a glass tube inserted inside a household microwave apparatus and irradiating until the evolution of H2S ceased. An interesting application of this method is the preparation of liquid crystals and other ferro- and antiferroelectric material such as compound 33 (Scheme 10). 

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