Quantum algorithm for total least squares data fitting

Least Squares Fitting of Data

This is the usual introduction to least squares fit by a line when the data represents measurements where the y–component is assumed to be functionally dependent on the x–component. Given a set of samples {(xi, yi)}i=1, determine A and B so that the line y = Ax + B best fits the samples in the sense that the sum of the squared errors between the yi and the line values Axi + B is minimized. Note...

Unifying Least Squares, Total Least Squares and Data Least Squares

The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the vector b and/or the matrix A such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to b, while in data least squares (DLS) it is restricted to A. In scaled total least squares (Scaled TLS) [15], corrections to both b and A are allowed, ...

PEDOMODELS FITTING WITH FUZZY LEAST SQUARES REGRESSION

Pedomodels have become a popular topic in soil science and environmentalresearch. They are predictive functions of certain soil properties based on other easily orcheaply measured properties. The common method for fitting pedomodels is to use classicalregression analysis, based on the assumptions of data crispness and deterministic relationsamong variables. In modeling natural systems such as s...

Least-Squares Fitting of Data with Polynomials

Least squares fitting

Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems C. A. Cantrell National Center for Atmospheric Research, Atmospheric Chemistry Division, 1850 Table Mesa Drive, Boulder, CO 80305, USA Received: 13 February 2008 – Accepted: 21 February 2008 – Published: 1 April 2008 Correspondence to: C. A. Cantrell ([email protected]) P...