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Standard method like Gauss elimination can be used to solve the matrix equation for .A more numerically stable method is provided by QR decomposition method. Since the matrix is a symmetric positive definite matrix, can be solved twice as fast with the Cholesky decomposition, while for large sparse systems conjugate gradient method is more effective.
Geometrically, we can see this problem by the following simple case where is a one-dimensional subspace: We want to find the closest approximation to the vector x {\displaystyle x} by a vector x ^ {\displaystyle {\hat {x}}} in the space W {\displaystyle W} .
Protein folding problem: Is it possible to predict the secondary, tertiary and quaternary structure of a polypeptide sequence based solely on the sequence and environmental information? Inverse protein-folding problem: Is it possible to design a polypeptide sequence which will adopt a given structure under certain environmental conditions?
MMSE can refer to: Mini–mental state examination, a questionnaire to measure cognitive impairment; Minimum mean square error, an estimation method that minimizes the mean square error; Multimedia Messaging Service Environment, the servers in a mobile telephony network required for Multimedia Messaging Service messaging.
The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
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It is used in analytical chemistry to increase the volatility of analytes, e.g., for gas chromatography. [1] It is also used to introduce the trimethylsilyl protecting group in organic synthesis. [2] A related reagent is N,O-bis(trimethylsilyl)trifluoroacetamide (BSTFA).
Thus, solutions of the boundary value problem correspond to solutions of the following system of N equations: (;,) = (;,) = (;,) =. The central N−2 equations are the matching conditions, and the first and last equations are the conditions y(t a) = y a and y(t b) = y b from the boundary value problem. The multiple shooting method solves the ...