NOTES ON MULTIVARIATE PRE-WAVELET DECOMPOSITION

Notes on Multivariate Analysis

Notes on Decomposition Methods

4 More general decomposition structures 17 4.1 General examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 Framework for decomposition structures . . . . . . . . . . . . . . . . . . . . 19 4.3 Primal decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.4 Dual decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2...

On Multivariate Rational Function Decomposition

If K is a field, and g, h ∈ K(x) are rational functions of degree greater than one, then f = g ◦ h = g(h) is their (functional) composition, (g, h) is a (functional) decomposition of f , and f is a decomposable rational function. The univariate rational functional decomposition problem can be stated as follows: given f ∈ K(x), determine whether there exists a decomposition (g, h) of f with g an...

On Construction of Multivariate Wavelet Frames

Construction of wavelet frames with matrix dilation is studied. We found a necessary condition and a sufficient condition under which a given pair of refinable functions generates dual wavelet systems with a given number of vanishing moments. For image compression and some other applications, it is very desirable to have wavelets with vanishing moment property. In particular, vanishing moments ...

Notes on the Singular Value Decomposition

NOTE: I have not thoroughly proofread these notes!!! We recommend the reader review Weeks 9-11 of Linear Algebra: Foundations to Frontiers-Notes to LAFF With.