K matrix method

The K-matrix method is essentially a configuration interaction (Cl) performed at a fixed energy lying in the continuum upon a basis of "unperturbed funetions that (at the formal level) includes both diserete and eontinuous subsets. It turns the Schrodinger equation into a system of integral equations for the K-matrix elements, which is then transformed into a linear system by a quadrature upon afinite L basis set. 

Klaproth, Martin H., 11 398 Klatte, Fritz, 25 628 Kleiner nitric acid process, 17 186 Klosterboer-Rutledge (KR) model, 19 356 Kluveromyces lactis, 12 479 genome of, 26 450t Klystrons, 23 135-136 K-matrix methods, 14 239 Kneading process, in paper recycling, 21 439 440... 

The L2 K-matrix method [191, 192] is a technique to carry out configuration interaction in the continuum, on the line of the pioneering paper by... 

Fano [96]. The K-matrix method has been successfully applied to a number of problems in atomic physics [167,193], particularly in conjunction with 13-splines [75,194-200]. B-splines are a convenient tool to represent accurately in finite boxes the radial component of continuum atomic orbitals [82], their major feature being a property known as effective completeness [201]. 

The B-spline K-matrix method follows the close-coupling prescription a complete set of stationary eigenfunctions of the Hamiltonian in the continuum is approximated with a linear combination of partial wave channels (PWCs) [Pg.286]

T.K. Fang, T.N. Chang, B-spline-based multichannel K-matrix method for atomic photo ionization, Phys. Rev. A 61 (2000) 062704. 

Mathematics of P and K Matrix Methods. Two basic forms of the matrix approach are in use, the so-called "K" and "P" matrix methods. Both methods involve using mixtures of known compositions as standards, then estimating concentrations in unknown mixtures using a set of calibration coefficients generated from the standard spectra. At each wavelength of the spectrum and for each calibration mixture, an extended form of Beer s law can be written as follows ... 

Application of both these techniques to extensive sets of binary and ternary acqueous solutions of albumin, IgG and fibrinogen indicated that the "P" matrix estimates of unknown compositions were more accurate than those made using the "K" matrix method. The "P matrix also allowed quantitation inspite of the uncertainty in water subtraction and the definition of baselines. 

The improvement in computer technology associated with spectroscopy has led to the expansion of quantitative infrared spectroscopy. The application of statistical methods to the analysis of experimental data is known as chemometrics [5-9]. A detailed description of this subject is beyond the scope of this present text, although several multivariate data analytical methods which are used for the analysis of FTIR spectroscopic data will be outlined here, without detailing the mathematics associated with these methods. The most conunonly used analytical methods in infrared spectroscopy are classical least-squares (CLS), inverse least-squares (ILS), partial least-squares (PLS), and principal component regression (PCR). CLS (also known as K-matrix methods) and PLS (also known as P-matrix methods) are least-squares methods involving matrix operations. These methods can be limited when very complex mixtures are investigated and factor analysis methods, such as PLS and PCR, can be more useful. The factor analysis methods use functions to model the variance in a data set. 

Calculation of concentrations therefore requires two matrix inverse calculations. This method is often referred to in the literature as the k matrix method of multilinear regression. The advantage of the technique is that it uses more variables (absorbances) than there are reference samples. In this sense, the solution is said to over-determined. 

The p and k matrix methods are two classical least squares approaches to multicomponent calibration. There are techniques based on factor analysis, however, that are increasingly popular these include the... 

The operations described in this section are known as classical least-squares (CLS) regression, or sometimes the K-matrix method of quantitative analysis. 

This method, known as the K-matrix method by spectroscopists, minimizes spectral errors [109,110]. 

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