K-Norm

Potassium Chloride. Camcopot Chloropotassuril Chlorvescent Diffu -K Enseal potassium chloride Kaleorid Kalitabs Kalium -Duriles Kaon-Cl Kaskay Kayback Kay -Cce-L K-Contin Klor-Con K-Norm K-Tab Len-to-Kalium Leo K Micro K Nu-K Peter-Kal Pfiklor Potavescent Re k a wail, Repone K Slow-K Spen-K. C1K mol wt 74.55. Cl 47.56%. K 52.44%. KO. Occurs in nature as the mineral sylvlne or syfvire. Industrial prepns Faith, Keyes St Clark s Industrial Chemicals, F. A. Lowen-torn, M. K. Moran, Eds. (Wiley-Interscience, New York, 4th ed., 1975) pp 666-673. 

Forward Analysis In this type of analysis, we are interested in the propagation of initial perturbations Sxq along the flow of (1), i.e., in the growth of the perturbations 5x t xo) = (xo -h Sxq) — xq. The condition number K,(t) may be defined as the worst case error propagation factor (cf. textbook [4]), so that, in first order perturbation analysis and with a suitable norm j ... 

Theorem 1.6. A bounded set of the space dual of the separable normed one is -k-weakly compact. 

The norm is useful when doing numerical calculations. If the computer s floating-point precision is 10" , then K = 10 indicates an ill-conditioned matrix. If the floating-point precision is I0" (double precision), then a matrix with K = I0 may be ill-conditioned. Two other measures are useful and are more easily calculated ... 

Residual minimization method (RMM-DIIS). Wood and Zunger [27] proposed lo minimize the norm of the residual vector instead of the Rayleigh quotient. This is an unconstrained minimization condition. Each minimization step starts with the evaluation of the preconditioned residual vector K for the approximate eigenstate... 

In this regard, rounding errors can be treated as possible perturbations of the right-hand side of equation (1) at every step. The iteration scheme (14) with parameters (29), (41) or (42) becomes unstable with respect to the right-hand side by exactly the same reasoning as before the norm of the operator Sk = E — Tf.A for the transition from the k — l)th iteration to the fcth iteration may exceed 1 for negative values of tf., since... 

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