英语词汇“least squares”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

least squares n. Mathematics the method of least squares (see square n. 8b); frequently attributive.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > [noun] > division > divisor or dividend > without remainder

partc1300

quotea1464

divisor1557

aliquot part1570

greatest common measure1570

measure1570

multiplex1570

aliquot1610

multiple1685

submultiple1702

least common multiple1714

bipartient1819

least squares1847

1847 Astronomische Nachrichten No. 599. 379 The solution by least squares.

1921 Biometrika 13 297 The fit by least squares to the means of the arrays is precisely the same as the fit by least squares to the whole swarm of points.

2014 Publ. Astron. Soc. Pacific 126 588/1 One can therefore identify an unknown tip-tilt..by direct projection on the basis of modes, or using a least squares algorithm.

b. method (also principle) of least squares [translating French méthode des moindres quarrés (A.-M. Legendre Nouvelles Méthodes pour la Détermination des Orbites des Comètes (1806) 74)] , the technique of estimating a quantity, fitting a graph to a set of experimental values, etc., so as to minimize the sum of the squares of the differences between the observed data and their estimated true values; so least square(s) attributive, denoting estimates, regression lines, etc., obtained by this method, the method itself, and the processes which it involves.

ΘΚΠ

the world > relative properties > number > probability or statistics > [noun] > population > numerical characteristic of > method used to estimate

method (also principle) of least squares1825

estimator1939

1812 Philos. Mag. 39 242 M. Legendre had not in any way mentioned the method which he has denominated that of small squares, (moindres carrées,).

1812 Philos. Mag. 39 243 The principle of the small squares.]

1825 Philos. Mag. 65 10 The principle of least squares will hold good, whatever law of probability be adopted.

1829 tr. S. D. Poisson in Q. Jrnl. Sci. & Arts July 96 This embarrassment..remained to the period when M. Legendre proposed a direct and uniform method of forming the final equations, which was generally adopted under the name of Method of least squares of the errors, which was assigned to it by its author.

1872 W. Thomson & P. G. Tait Treat. Nat. Philos. i. iii. 115 A and B are to be found by the method of least squares from values of l observed for different given values of t.

1916 L. D. Weld Theory of Errors & Least Squares v. 87 If more [observations] are made, least-square reduction may be applied to their adjustment.

1939 A. E. Treloar Elem. Statistical Reasoning iv. 59 ‘Least squares’ solutions, or the minimizing of squared deviations to reach representative values, may be made with facility, whereas the minimizing of absolute deviations becomes so involved that the problems can rarely be solved that way.

1950 A. McF. Mood Introd. Theory Statistics xiii. 311 The primary reason that the method of least squares is commonly used for curve fitting is merely that it leads to a simple linear system of equations for determining the coefficients.

1957 G. E. Hutchinson Treat. Limnol. I. vii. 469 C is determined from the distribution of temperatures by the method of least squares.

1970 Jrnl. Gen. Psychol. July 127 The principle of the method is to rotate one matrix (usually a principal-components matrix) as close as possible to a hypothesized factor matrix, in a least-square solution.

1974 Encycl. Brit. Macropædia VII. 967/1 Gauss developed a technique for calculating its orbital components with such accuracy that several astronomers late in 1801 and early in 1802 were able to locate Ceres again without difficulty. As part of his technique, Gauss used his method of least squares, developed about 1794.

单词	least squares
释义	> as lemmas least squares least squares n. Mathematics the method of least squares (see square n. 8b); frequently attributive. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > [noun] > division > divisor or dividend > without remainder partc1300 quotea1464 divisor1557 aliquot part1570 greatest common measure1570 measure1570 multiplex1570 aliquot1610 multiple1685 submultiple1702 least common multiple1714 bipartient1819 least squares1847 1847 Astronomische Nachrichten No. 599. 379 The solution by least squares. 1921 Biometrika 13 297 The fit by least squares to the means of the arrays is precisely the same as the fit by least squares to the whole swarm of points. 2014 Publ. Astron. Soc. Pacific 126 588/1 One can therefore identify an unknown tip-tilt..by direct projection on the basis of modes, or using a least squares algorithm. extracted from leastadj.pron.n.adv. least square(s) b. method (also principle) of least squares [translating French méthode des moindres quarrés (A.-M. Legendre Nouvelles Méthodes pour la Détermination des Orbites des Comètes (1806) 74)] , the technique of estimating a quantity, fitting a graph to a set of experimental values, etc., so as to minimize the sum of the squares of the differences between the observed data and their estimated true values; so least square(s) attributive, denoting estimates, regression lines, etc., obtained by this method, the method itself, and the processes which it involves. ΘΚΠ the world > relative properties > number > probability or statistics > [noun] > population > numerical characteristic of > method used to estimate method (also principle) of least squares1825 estimator1939 1812 Philos. Mag. 39 242 M. Legendre had not in any way mentioned the method which he has denominated that of small squares, (moindres carrées,). 1812 Philos. Mag. 39 243 The principle of the small squares.] 1825 Philos. Mag. 65 10 The principle of least squares will hold good, whatever law of probability be adopted. 1829 tr. S. D. Poisson in Q. Jrnl. Sci. & Arts July 96 This embarrassment..remained to the period when M. Legendre proposed a direct and uniform method of forming the final equations, which was generally adopted under the name of Method of least squares of the errors, which was assigned to it by its author. 1872 W. Thomson & P. G. Tait Treat. Nat. Philos. i. iii. 115 A and B are to be found by the method of least squares from values of l observed for different given values of t. 1916 L. D. Weld Theory of Errors & Least Squares v. 87 If more [observations] are made, least-square reduction may be applied to their adjustment. 1939 A. E. Treloar Elem. Statistical Reasoning iv. 59 ‘Least squares’ solutions, or the minimizing of squared deviations to reach representative values, may be made with facility, whereas the minimizing of absolute deviations becomes so involved that the problems can rarely be solved that way. 1950 A. McF. Mood Introd. Theory Statistics xiii. 311 The primary reason that the method of least squares is commonly used for curve fitting is merely that it leads to a simple linear system of equations for determining the coefficients. 1957 G. E. Hutchinson Treat. Limnol. I. vii. 469 C is determined from the distribution of temperatures by the method of least squares. 1970 Jrnl. Gen. Psychol. July 127 The principle of the method is to rotate one matrix (usually a principal-components matrix) as close as possible to a hypothesized factor matrix, in a least-square solution. 1974 Encycl. Brit. Macropædia VII. 967/1 Gauss developed a technique for calculating its orbital components with such accuracy that several astronomers late in 1801 and early in 1802 were able to locate Ceres again without difficulty. As part of his technique, Gauss used his method of least squares, developed about 1794. extracted from squaren. < as lemmas
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