Orthonormal basis in the space $C_{1}[0,1]$

Building an Orthonormal Basis, Revisited

Frisvad [2012b] describes a widely-used computational method for efficiently augmenting a given single unit vector with two other vectors to produce an orthonormal frame in three dimensions, a useful operation for any physically based renderer. However, the implementation has a precision problem: as the z component of the input vector approaches −1, floating point cancellation causes the frame ...

An Orthonormal Basis for Entailment

Entailment is a logical relationship in which the truth of a proposition implies the truth of another proposition. The ability to detect entailment has applications in IR, QA, and many other areas. This study uses the vector space model to explore the relationship between cohesion and entailment. A Latent Semantic Analysis space is used to measure cohesion between propositions using vector simi...

Modelling with Orthonormal Basis Functions

System identification with generalized orthonormal basis functions

A least-squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions. The basis functions are orthogonal in 8$, and generalize the pulse, Laguerre and Kautz bases. One of their important properties is that, when chosen properly, ...

Improved accuracy when building an orthonormal basis

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.