The Accuracy of Least Squares Solutions: Part II: The Standard Deviation of the Errors of Linear Equations of Condition.
نویسنده
چکیده
Often we know the results of n observations, Cl'... c,', such that ci/ may be supposed to have been drawn at random from a normal universe of unknown standard deviation a (the same for all the observations), and with mean ajta + bj4 + djid + . . . + mijm. Here the coefficients as . .. mi are supposed to be known, while the m quantities za ... are unknown. We suppose that n > m, and the question that immediately arises is (A): If we know only the values of ci' and of ai, bi, etc., what are the values of the t 's? The answer to question (A) has been given' in a previous paper (referred to henceforth as Part I) in these PROCEEDINGS. The next question, perhaps, in order of importance is (B): If we know only the values of ci' and of ai, bi, etc., what is the value of a? The classical answer to the problem is well known; it is furnished by the method of least squares. In the notation of Part I,
منابع مشابه
Theory of block-pulse functions in numerical solution of Fredholm integral equations of the second kind
Recently, the block-pulse functions (BPFs) are used in solving electromagnetic scattering problem, which are modeled as linear Fredholm integral equations (FIEs) of the second kind. But the theoretical aspect of this method has not fully investigated yet. In this article, in addition to presenting a new approach for solving FIE of the second kind, the theory of both methods is investigated as a...
متن کاملInverse modeling of gravity field data due to finite vertical cylinder using modular neural network and least-squares standard deviation method
In this paper, modular neural network (MNN) inversion has been applied for the parameters approximation of the gravity anomaly causative target. The trained neural network is used for estimating the amplitude coefficient and depths to the top and bottom of a finite vertical cylinder source. The results of the applied neural network method are compared with the results of the least-squares stand...
متن کاملPositive solution of non-square fully Fuzzy linear system of equation in general form using least square method
In this paper, we propose the least-squares method for computing the positive solution of a $mtimes n$ fully fuzzy linear system (FFLS) of equations, where $m > n$, based on Kaffman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of the fuzzy number vector solution of ...
متن کاملFuzzy Hybrid least-Squares Regression Approach to Estimating the amount of Extra Cellular Recombinant Protein A from Escherichia coli BL21
Introduction: Immune Protein A is a component with a vast spectrum of biochemical, biological and medical usages. The coding gene of this protein was extracted from Staphylococcus aureus and was cloned and expressed in Escherichia coli bacteria. Suitable statistical methods are utilized to optimize expression conditions for evaluating experiment accuracy , guarantee the accuracy of subsequent ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 20 12 شماره
صفحات -
تاریخ انتشار 2005