Stability of numerical processes

Numerical modelling of microforming processes

It is well recognized that expertise, experience, and theoretical knowledge available in conventionally sized metal forming cannot be simply transferred to microforming. This is due to so-called size effects which have distinct effect on material flow, friction and other process characteristics [1,2]. Today, process simulation is a standard tool in industry, applied to support process layout an...

Notes on Numerical Stability

Correctness in the presence of error (e.g., when floating point computations are performed) takes on a different meaning. For many problems for which computers are used, there is one correct answer and we expect that answer to be computed by our program. The problem is that most real numbers cannot be stored exactly in a computer memory. They are stored as approximations, floating point numbers...

Numerical stability of surface implicitization

In geometric modelling surfaces can be given essentially in two ways: implicit and parametric form. The automatic transition between the implicit and the parametric representations of surfaces is of fundamental importance. In the literature there are several symbolic/numeric implicitization techniques based on resultants [1], Gröbner–basis [2], moving surfaces [3], linear algebra [4], but the n...

Numerical stability of fast trigonometrictransformsDaniel

This paper presents stability results for various fast trigonometric transforms. We consider the numerical stability of the classical fast Fourier transform (FFT) with respect to diierent precomputation methods for the involved twiddle factors and show the strong innuence of precomputation errors on the numerical stability of the FFT. The examinations are extended to fast algorithms for the com...

Numerical Solution of Parabolized Stability Equations Using Super Compact Scheme