Improved accuracy when building an orthonormal basis

نویسنده

  • Nelson Max
چکیده

Frisvad’s method for building a 3D orthonormal basis from a unit vector has accuracy problems in its published floating point form. These problems are investigated and a partial fix is suggested, by replacing the threshold 0.9999999 by the threshold -0.999805696, which decreases the maximum error in the orthonormality conditions from 0.623 to 0.0062.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Frequency Domain Estimation Using Orthonormal Bases

This paper examines the use of general orthonormal bases for system identification from frequency domain data. This idea has been studied in great depth for the particular case of the orthonormal trigonometric basis. Here we show that the accuracy of the estimate can be significantly improved by rejecting the trigonometric basis in favour of a more general orthogonal basis that is able to be ad...

متن کامل

Constructing Two-Dimensional Multi-Wavelet for Solving Two-Dimensional Fredholm Integral Equations

In this paper, a two-dimensional multi-wavelet is constructed in terms of Chebyshev polynomials. The constructed multi-wavelet is an orthonormal basis for space. By discretizing two-dimensional Fredholm integral equation reduce to a algebraic system. The obtained system is solved by the Galerkin method in the subspace of by using two-dimensional multi-wavelet bases. Because the bases of subs...

متن کامل

The fundamental role of general orthonormal bases in system identification

The purpose of this paper is threefold. Firstly, it is to establish that contrary to what might be expected, the accuracy of well known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure. Secondly, it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any f...

متن کامل

Improved and Quantified Accuracy for Linear Spectral Estimates

In the context of spectral estimation, this paper examines the use of an ‘orthonormal basis’ wherein prior knowledge (in the form of fixed poles) may be incorporated in the solution and FIR structures are then seen as a special case of implicitly involving prior knowledge of all poles at the origin. The main technical results are ones that quantify the accuracy of the resulting spectral estimat...

متن کامل

A numerical study of electrohydrodynamic flow analysis in a circular cylindrical conduit using orthonormal Bernstein polynomials

In this work, the nonlinear boundary value problem in electrohydrodynamics flow of a fluid in an ion-drag configuration in a circular cylindrical conduit is studied numerically. An effective collocation method, which is based on orthonormal Bernstein polynomials is employed to simulate the solution of this model. Some properties of orthonormal Bernstein polynomials are introduced and utilized t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017