Final versiongauss and the method of least squares

Final versiongauss and the method of least squares - Gauss...

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1 Gauss and the Method of Least Squares Teddy Petrou  Hongxiao Zhu
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2    Outline Who was Gauss? Why was there controversy in finding the method of least  squares? Gauss’ treatment of error Gauss’ derivation of the method of least squares Gauss’ derivation by modern matrix notation Gauss-Markov theorem Limitations of the method of least squares References
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3 Johann Carl Friedrich Gauss      Born:1777 Brunswick, Germany   Died: February 23, 1855, Göttingen, Germany      By the age of eight during arithmetic class he  astonished his teachers by being able to  instantly find the sum of the first hundred  integers.
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4 Facts about Gauss Attended Brunswick College in 1792, where he  discovered many important theorems before even  reaching them in his studies Found a square root in two different ways to fifty  decimal places by ingenious expansions and  interpolations Constructed a regular 17 sided polygon, the first  advance in this matter in two millennia. He was only  18 when he made the discovery
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5 Ideas of Gauss Gauss was a mathematical scientist with interests in so many  areas as a young man including theory of numbers, to algebra,  analysis, geometry, probability, and the theory of errors. His interests grew, including observational astronomy, celestial  mechanics, surveying, geodesy, capillarity, geomagnetism,  electromagnetism, mechanism optics, and actuarial science.
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6 Intellectual Personality and Controversy Those who knew Gauss best found him to be cold and       uncommunicative. He only published half of his ideas and found no one to share  his most valued thoughts. In 1805 Adrien-Marie Legendre published a paper on the  method of least squares. His treatment, however, lacked a  ‘formal consideration of probability and it’s relationship to least  squares’, making it impossible to determine the accuracy of the  method when applied to real observations. Gauss claimed that he had written colleagues concerning the  use of least squares dating back to 1795
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7 Formal Arrival of Least Squares Gauss     Published  ‘The theory of the Motion of Heavenly Bodies’  in 1809 He gave a probabilistic justification of the method,which was  based on the assumption of a normal distribution of errors.  Gauss himself later abandoned the use of normal error function.   Published  ‘Theory of the Combination of Observations Least  Subject to Errors’  in 1820s.  He substituted the root mean square  error for Laplace’s mean absolute error. Laplace   
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Final versiongauss and the method of least squares - Gauss...

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