Stretching the Least Squares to Embed Loss Functions Tables

A Least Squares Approach to Estimating the Average Reservoir Pressure

Least squares method (LSM) is an accurate and rapid method for solving some analytical and numerical problems. This method can be used to estimate the average reservoir pressure in well test analysis. In fact, it may be employed to estimate parameters such as permeability (k) and pore volume (Vp). Regarding this point, buildup, drawdown, late transient test data, modified Muskat method, interfe...

Repeated Knots in Least Squares Multiquadric Functions

A previous paper by the authors [FH93] noted that there was a strong tendency to obtain near-repeated knots in their algorithm for least squares approximation of scattered data by multiquadric functions. In this paper we observe that this leads naturally to the inclusion of derivatives of the multiquadric basis function in the approximation, and give an algorithm for accomplishing this. A compa...

Least Squares and Entropy as Penalty Functions

Mathematical measures of entropy as defined by Shannon (1948) and Kullback and Leibler (1951) are currently in vogue in the field of econometrics, primarily due to the comprehensive work by Golan, Judge, and Miller (1996). In this paper, an alternative interpretation of the entropy measure as a penalty function over deviations is presented. Using this interpretation, a number of parallels are d...

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, ...

Least squares surface approximation to scattered data using multiquadratic functions