Newton-Gauss nonlinear least-squares

The determination of the pAa of a nucleobase by potentiometry relies on differences in NaOH consumptions between titrations of HN03 carried out in the absence and presence of the compound whose p/fa is to be obtained (208). Curve-fit procedures using Newton-Gauss nonlinear least-squares programs are applied to calculate the pA"a value. 

Kinetic curves were analyzed and the further correlations were determined with a nonlinear least-square-method PC program, working with the Gauss-Newton method. 

The most effective spectrophotometric procedures for pKa determination are based on the processing of whole absorption curves over a broad range of wavelengths, with data collected over a suitable range of pH. Most of the approaches are based on mass balance equations incorporating absorbance data (of solutions adjusted to various pH values) as dependent variables and equilibrium constants as parameters, refined by nonlinear least-squares refinement, using Gauss-Newton, Marquardt, or Simplex procedures [120-126,226],... 

Kinetic parameters were determined by following the reduction of the nicotinamide coenzymes at 340 nm as described by Dean and Dvorak (7). Rates were calculated using a molar extinction coefficient for NAD(P)H of 6200 M f cm" and protein concentrations were determined at 280 nm using a molar extinction coefficient of 30,420 M cm f Nonlinear least squares Gauss-Newton regressions were used to determine the fit of the data to the Michaelis-Menten model. 

In general, the error e tic-q-i+j, 0) is a non-linear function of the parameter vector 0. Therefore, the above problem is a well-known nonlinear least squares problem (NLSP) that may be solved by various optimisation algorithms such as the Levenberg-Marquardt algorithm [2], the quasi-Newton method or the Gauss-Newton (GN) algorithm [3]. 

Least-squares methods are usually used for fitting a model to experimental data. They may be used for functions consisting of square sums of nonlinear functions. The well-known Gauss-Newton method often leads to instabilities in the minimization process since the steps are too large. The Marquardt algorithm [9 1 is better in this respect but it is computationally expensive. 

Linear and nonlinear regression analyses, including least squares, estimated vector of parameters, method of steepest descent, Gauss-Newton method, Marquardt Method, Newton Method,... 

Least squares multiple nonlinear regression using the Marquardt and Gauss-Newton methods. The program can fit simultaneous ordinary differential equations and/or algebraic equations to multiresponse data. 

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