We examine the question of when a polynomial f over a commutative ring has a nontrivial functional decomposition f = g ◦ h. Previous algorithms [2, 3, 1] are exponential-time in the worst case, require polynomial factorization, and only work over fields of characteristic 0. We present an O(n2)-time algorithm. We also show that the problem is in NC . The algorithm does not use polynomial factori...

We investigate the effect of load balancing when performing Cholesky factorization on a massively parallel SIMD computer. In particular we describe a supernodal algorithm for performing sparse Cholesky factorization. The way the matrix is mapped onto the processors has significant effect on its efficiency. We show that this assignment problem can be modeled as a graph coloring problem in a weig...

This tutorial is concerned with the structure and motion estimation from the sequence of images taken with an uncalibrated affine camera. This problem was first addressed by Koenderink and van Doorn [1]. We will address the following problems: • Calibrated and uncalibrated affine camera models; • Tomasi and Kanade factorization method; • Sequential estimation of the structure and motion paramet...

We summarize the main known properties of factorization-based projective structure from motion, including the basic formulation, depth estimation and how it can sometimes be avoided, and some suggestions about statistical properties.

Results on diiractive dijet and W-boson production from CDF are reviewed and compared with predictions based on factorization of the diiractive structure function of the proton measured in deep inelastic scattering at HERA.

The Symmetric Delay Factorization (SDF) is introduced in 1] for synthesizing linear phase paraunitary lter banks and is applied successfully in 2] for designing Time-Varying Filter Banks (TVFB). This paper describes a minimal and complete generalized symmetric delay factorization valid for a larger class of paraunitary lter banks, and for an arbitrary (even and odd) number of channels. The appr...

Two recent approaches [4, 14] in subspace identification problems require the computation of the R factor of the QR factorization of a block–Hankel matrix H , which, in general has a huge number of rows. Since the data are perturbed by noise, the involved matrix H is, in general, full rank. It is well known that, from a theoretical point of view, the R factor of the QR factorization of H is equ...

We systematically investigate the factorization of causal finite impulse response (FIR) paraunitary filterbanks with given filter length. Based on the singular value decomposition of the coefficient matrices of the polyphase representation, a fundamental order-one factorization form is first proposed for general paraunitary systems. Then, we develop a new structure for the design and implementa...

Matrix factorization methods are now widely used to recover 3D structure from 2D projections [1]. In practice, the observation matrix to be factored out has missing data, due to the limited field of view and the occlusion that occur in real video sequences. In opposition to the optimality of the SVD to factor out matrices without missing entries, the optimal solution for the missing data case i...

Keyword: Factorization method Self-adjoint differential equations Eigenvalue problems This paper deals with the factorization of self-adjoint differential operators Lð2nÞ 1⁄4 1 q d n dx qb d n dx , and their spectral type differential equations. Sufficient conditions of factorization are reported. A large class of differential operators and equations that can be factorized is obtained. The fact...