A family of tests for periodic components in a white Gaussian series is proposed. The test is based on a statistic which is proportional to the ratio of the maximum periodogram to the trimmed mean of the periodograms. The ...

Finding the unconstrained minimizer of a function of more than one variable is an important problem with many practical applications, including data fitting, engineering design, and process control. In addition, techniques ...

In this paper, we investigate the role of the secant or quasi-Newton condition in the sparse Broyden or Schubert update method for solving systems of nonlinear equations whose Jacobians are either sparse, or can be approximated acceptably by conveniently sparse matrices. We develop a general theory on perturbations to the secant equation that will still allow a proof of local q-linear convergence. To illustrate the theory, we show how to generalize the standard secant condition to the case when the function difference is contaminated by noise....

Quasi-Newton methods are well known iterative methods for solving nonlinear problems. At each stage, a system of linear equations has to be solved. However, for large scale problems, solving the linear system of equations ...

Many current algorithms for nonlinear constrained optimization problems determine a direction by solving a quadratic programming subproblem. The global convergence properties are addressed by using a line search technique ...

The axioms defining stochastic processes are generally simple. However, estimation of the parameters of a process from data is extremely difficult if customary techniques are used. This is due to the complexities involved ...

In this research we extend the Levenberg-Marquardt algorithm for approximating zeros of the nonlinear system F(x) = 0, where F is continuously differentiable from R^n to R^n. Instead of the l2-norm, arbitrary norms can ...

In this paper we describe the Nelder-Mead simplex method for obtaining the minimizer of a function. The Nelder-Mead algorithm has several properties that make it a natural choice for implementation and utilization on ...