Review/Outline Recall: If all bunches of d − 1 columns of a... are linearly independent, then the minimum
... For fixed choice of irreducible P of degree k with coefficients in Fp , the corresponding computational model of Fpk is Fpk = {reduced polynomials mod P (x)} addition given by polynomial addition (which does not increase degree), multiplication given by polynomial multiplication followed by reductio ...
... For fixed choice of irreducible P of degree k with coefficients in Fp , the corresponding computational model of Fpk is Fpk = {reduced polynomials mod P (x)} addition given by polynomial addition (which does not increase degree), multiplication given by polynomial multiplication followed by reductio ...
Some known results on polynomial factorization over towers of field
... γ ∈ S[t] of (f1 , . . . , fℓ ) such that ϕ0 (γ) 6= 0. Taking it for granted, let α ∈ S[t] be such that ϕ0 (α) 6= 0 and αgℓ+1 is in S[t, x1 , . . . , xℓ+1 ]. Then, applying the characteristic property of γ, we see that αγhe fℓ+1 is in S[t, x1 , . . . , xℓ+1 ], for some integer e ≥ 0, where h = h1 · · ...
... γ ∈ S[t] of (f1 , . . . , fℓ ) such that ϕ0 (γ) 6= 0. Taking it for granted, let α ∈ S[t] be such that ϕ0 (α) 6= 0 and αgℓ+1 is in S[t, x1 , . . . , xℓ+1 ]. Then, applying the characteristic property of γ, we see that αγhe fℓ+1 is in S[t, x1 , . . . , xℓ+1 ], for some integer e ≥ 0, where h = h1 · · ...
Nonsymmetric algebraic Riccati equations and Wiener
... found numerically by iterative methods [3, 7, 10, 12, 13, 19] and subspace methods ...
... found numerically by iterative methods [3, 7, 10, 12, 13, 19] and subspace methods ...
Relative perturbation theory for diagonally dominant matrices
... Our study of small componentwise relative perturbations assumes that the zero off-diagonal entries incur no perturbation. Although this assumption is key for the error analysis [14] of the algorithm presented in [45], it may be restrictive in some problems. However, in many applications (e.g., disc ...
... Our study of small componentwise relative perturbations assumes that the zero off-diagonal entries incur no perturbation. Although this assumption is key for the error analysis [14] of the algorithm presented in [45], it may be restrictive in some problems. However, in many applications (e.g., disc ...
Preconditioning stochastic Galerkin saddle point
... (SG) mixed finite element formulations of two-field PDE problems with random coefficients. Examples include the Darcy flow problem with random permeability coefficients and the Stokes problem with random viscosity. A0 , A1 , . . . , AN and B are finite element matrices associated with the physical d ...
... (SG) mixed finite element formulations of two-field PDE problems with random coefficients. Examples include the Darcy flow problem with random permeability coefficients and the Stokes problem with random viscosity. A0 , A1 , . . . , AN and B are finite element matrices associated with the physical d ...
![arXiv:math/0604168v1 [math.CO] 7 Apr 2006](http://s1.studyres.com/store/data/017890502_1-2c1abc75bd42752544cdf6d7b46b6ed7-300x300.png)
arXiv:math/0604168v1 [math.CO] 7 Apr 2006
... A, we construct an arrangement by simplifying, that is, removing all zero columns, constructing a multiset of hyperplanes corresponding to the kernels of the linear forms defined by the columns, giving a multiarrangement, and disregarding the multiplicities to obtain an arrangement. If A is essentia ...
... A, we construct an arrangement by simplifying, that is, removing all zero columns, constructing a multiset of hyperplanes corresponding to the kernels of the linear forms defined by the columns, giving a multiarrangement, and disregarding the multiplicities to obtain an arrangement. If A is essentia ...
Group Theory – Crash Course 1 What is a group?
... group structure. This endows them with a vivid geometric meaning. Therefore it is worth to work through a bit more mathematical formalism, in order to understand these statements. Let us start with manifolds. I will not give the rigorous mathematical definition. For our purpose a manifold is a space ...
... group structure. This endows them with a vivid geometric meaning. Therefore it is worth to work through a bit more mathematical formalism, in order to understand these statements. Let us start with manifolds. I will not give the rigorous mathematical definition. For our purpose a manifold is a space ...
Non-negative matrix factorization
NMF redirects here. For the bridge convention, see new minor forcing.Non-negative matrix factorization (NMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.NMF finds applications in such fields as computer vision, document clustering, chemometrics, audio signal processing and recommender systems.