The interpolation of a planar sequence of points p0, . . . , pN by shape-preserving G 1 or G2 PH quintic splines with specified end conditions is considered. The shape-preservation property is secured by adjusting ‘tension’ parameters that arise upon relaxing parametric continuity to geometric continuity. In the G2 case, the PH spline construction is based on applying Newton–Raphson iterations ...

In this paper we present a duality approach for finding a robust best approximation from a set involving interpolation constraints and uncertain inequality constraints in a Hilbert space that is immunized against the data uncertainty using a nonsmooth Newton method. Following the framework of robust optimization, we assume that the input data of the inequality constraints are not known exactly ...

A method for variable-rate data sampling is proposed for the purpose of low-power data acquisition in a small footprint microsystem. The procedure enables energy saving by utilizing dynamic power management techniques and is based on the Adams–Bashforth and Adams–Moulton multistep predictorcorrector methods for ordinary differential equations. Newton– Gregory backward difference interpolation f...

The analysis of unilateral sliding contact in elasticity is equivalent to a minimisation problem subjected to a set of inequality constraints. However, the presence of boundary discontinuities, such as those stemming from the spatial discretisation, appears as a major problem to determine the set of active constraints. This work introduces a smoothing technique of the master surface resorting t...

We present a new set of algorithms for computation of matrix rational interpolants and one-sided matrix greatest common divisors. Examples of these interpolants include Padé approximants, Newton–Padé, Hermite–Padé, and simultaneous Padé approximants, and more generally M-Padé approximants along with their matrix generalizations. The algorithms are fast and compute all solutions to a given probl...

The Keralese origin of these series is independent of the discovery in a later century of the inverse-tangent expansion [ A ] by JAMES GREGORY (1671) and GOTTFRIED WILHELM LEIBNIZ (1673), of the sine and cosine series by ISAAC NEWTON (1670) and LEIBNIZ (1676). The Malay~]am work Yukti-bhCtsa, where these series are found, belongs unquestionably to the sixteenth century, and there is not the sli...

We present a new, to our knowledge, method for extracting optical properties from integrating sphere measurements on thin biological samples. The method is based on multivariate calibration techniques involving Monte Carlo simulations, multiple polynomial regression, and a Newton-Raphson algorithm for solving nonlinear equation systems. Prediction tests with simulated data showed that the mean ...

To maximise the economic benefit, photovoltaic (PV) systems in general operate in the so-called maximum power point tracking (MPPT) mode. However, in certain occasions (e.g. in a microgrid or in a weak system), it is beneficial for a PV system not to always operate in the MPPT mode, but occasionally in the power dispatch mode, because of the top priority of maintaining system stability. To this...

The kinematic orbit is a time series of position vectors generally obtained from GPS observations. Velocity vector is required for satellite gravimetry application. It cannot directly be observed and should be numerically determined from position vectors. Numerical differentiation is usually employed for a satellite’s velocity, and acceleration determination. However, noise amplification is the...

In this thesis we explore recent methods for computing the Newton polytope of the implicit equation and study their applicability to the representation change from the parametric form to implicit. Computing a (super)set of the monomials appearing in the implicit equation allows us to determine the interpolation space. Following this phase we implement interpolation by exact or numeric linear al...