相关论文: Constructive updating/downdating of oblique projec…
A new way of orthogonalizing ensembles of vectors by "lifting" them to higher dimensions is introduced. This method can potentially be utilized for solving quantum decision and computing problems.
The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors, matrices, etc) into an orthonormal basis (a set of orthogonal, unit-length vectors, bi or tri dimensional matrices). The…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic…
The Gram-Schmidt algorithm produces a pairwise orthogonal set from a linearly independent set of vectors in an inner product vector space V. We give a linear algorithm that constructs vectors with the same span and which have pairwise the…
We are presenting a simple and numerical stable algorithm for the solution of the cone projection problem which is suitable for relative small data sets and for simulation purposes needed for convexity tests. Not even one pseudo-inverse…
We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact…
An approach is proposed which, given a family of linearly independent functions, constructs the appropriate biorthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves…
Pan-sharpening algorithms utilize a panchromatic image and a multispectral image to generate a high spatial and high spectral image. However, the optimizations of the algorithms are designed with different standards. We employ a simple…
The orthogonalization process is an essential building block in Krylov space methods, which takes up a large portion of the computational time. Commonly used methods, like the Gram-Schmidt method, consider the projection and normalization…
In this paper a generalization of the Gram-Schmidt Algorithm is presented. Actually we provide an algorithm to construct a set of equiangular vectors with a given angle $\theta\in(0,\arccos(\frac{-1}{n-1}))$ using a set of input independent…
We introduce a new method for the reconstruction of a function from linear measurements by means of oblique projections. The space spanned by the measurement vectors may be different from the subspace in which the function is reconstructed.…
We generalize classical orthogonalization procedures from real linear algebra to the setting of fermionic quantum (FQ) operations. In the case of the Gram-Schmidt orthogonalization procedure, the generalization is easy. This, however, helps…
Generalized alternating projections is an algorithm that alternates relaxed projections onto a finite number of sets to find a point in their intersection. We consider the special case of two linear subspaces, for which the algorithm…
An oblique projections based feedback stabilizability result in the literature is extended to a larger class of reaction-convection terms. A discussion is presented including a comparison between explicit oblique projections base feedback…
Signal reconstruction from a sample using an orthogonal projector onto a guiding subspace is theoretically well justified, but may be difficult to practically implement. We propose more general guiding operators, which increase signal…
A backward biorthogonalization approach is proposed, which modifies biorthogonal functions so as to generate orthogonal projections onto a reduced subspace. The technique is relevant to problems amenable to be represented by a general…
Three algorithms of Gram-Schmidt type are given that produce an orthogonal decomposition of finite $d$-dimensional symmetric, alternating, or Hermitian forms over division rings. The first uses $d^3/3+O(d^2)$ ring operations with very…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
A randomized Gram-Schmidt algorithm is developed for orthonormalization of high-dimensional vectors or QR factorization. The proposed process can be less computationally expensive than the classical Gram-Schmidt process while being at least…