A and B coefficients are given by formulas: B = b and A = exp(a) where:

a= |

b= |

skip to main |
skip to sidebar
## Thursday, January 27, 2011

###
Least Squares Fitting--Exponential

## Thursday, January 20, 2011

###
Least Squares Fitting

## About Me

## Certifications

Let's consider following functional form:

A and B coefficients are given by formulas: B = b and A = exp(a) where:

and

A and B coefficients are given by formulas: B = b and A = exp(a) where:

a= |

b= |

The term least squares describes a frequently used approach to solving overdetermined or inexactly specified systems of equations in an approximate sense. Instead of solving the equations exactly, we seek only to minimize the sum of the squares of the residuals.

The least squares criterion has important statistical interpretations. If appropriate probabilistic assumptions about underlying error distributions are made, least squares produces what is known as the maximum-likelihood estimate of the parameters. Even if the probabilistic assumptions are not satisfied, years of experience

have shown that least squares produces useful results.

The computational techniques for linear least squares problems make use of orthogonal matrix factorizations.

Lets consider function:

for estimation of coefficients a and b we can use following equations:

The least squares criterion has important statistical interpretations. If appropriate probabilistic assumptions about underlying error distributions are made, least squares produces what is known as the maximum-likelihood estimate of the parameters. Even if the probabilistic assumptions are not satisfied, years of experience

have shown that least squares produces useful results.

The computational techniques for linear least squares problems make use of orthogonal matrix factorizations.

Lets consider function:

for estimation of coefficients a and b we can use following equations:

double sumY = 0; double sumX = 0; double sumXY = 0; double sumX2 = 0; foreach (Sample s in samples) { sumY = sumY + s.y; sumX = sumX + s.x; sumX2 = sumX2 + s.x * s.x; sumXY = sumXY + s.x * s.y; } double a = (sumY * sumX2 - sumX * sumXY) / (samples.Count * sumX2 - (sumX * sumX)); double b = (samples.Count * sumXY - (sumX * sumY)) / (samples.Count * sumX2 - (sumX * sumX));

Subscribe to:
Posts (Atom)

- Robert Kanasz
- My name is Robert Kanasz and I have been working with ASP.NET, WinForms and C# for several years.

Powered by Blogger.

MCSD |
Web Applications |

MCSE |
Data Platform |

MCSA |
SQL Server 2012 |

MCTS |
.NET Framework 3.5, ASP.NET Applications SQL Server 2008, Database Development SQL Server 2008, Implementation and Maintenance .NET Framework 4, Data Access .NET Framework 4, Service Communication Applications .NET Framework 4, Web Applications |

MCPD |
ASP.NET Developer 3.5 Web Developer 4 |

MCITP |
Database Administrator 2008 Database Developer 2008 |

MS |
Programming in HTML5 with JavaScript and CSS3 Specialist |