相关论文: Rigorous Perturbation Bounds for the QX Decomposit…
This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization…
The implementation of the finite element method for linear elliptic equations requires to assemble the stiffness matrix and the load vector. In general, the entries of this matrix-vector system are not known explicitly but need to be…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
The main obstacle in describing inclusive decay spectra in QCD - which, in particular, limits the precision in extrapolating the measured \bar{B} \to X(s) gamma rate to the full phase space as well as in extracting |V_{ub}| from inclusive…
Combined perturbation bounds are presented for eigenvalues and eigenspaces of Hermitian matrices or singular values and singular subspaces of general matrices. The bounds are derived based on the smooth decompositions and elementary…
We consider a parametric convex quadratic programming, CQP, relaxation for the quadratic knapsack problem, QKP. This relaxation maintains partial quadratic information from the original QKP by perturbing the objective function to obtain a…
A new error bound for the linear complementarity problem is given when the involved matrix is a B-matrix. It is shown that this bound is sharper than some previous bounds [C.Q. Li, Y.T. Li. Note on error bounds for linear complementarity…
Renormalization factors for local vector and axial vector currents for the Wilson quark action are perturbatively calculated to one loop order including finite quark masses from the ratio of the on-shell quark matrix elements in the Feynman…
Perturbation analysis of Markov chains provides bounds on the effect that a change in a Markov transition matrix has on the corresponding stationary distribution. This paper compares and analyzes bounds found in the literature for finite…
Incomplete factorizations have long been popular general-purpose algebraic preconditioners for solving large sparse linear systems of equations. Guaranteeing the factorization is breakdown free while computing a high quality preconditioner…
The notion of a (polynomial) kernelization from parameterized complexity is a well-studied model for efficient preprocessing for hard computational problems. By now, it is quite well understood which parameterized problems do or…
We briefly summarize some recent theoretical developments in perturbative QCD, emphasizing new ideas which have led to widening the domain of applicability of perturbation theory. In particular, it is now possible to calculate efficiently…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
We study fine-grained error bounds for differentially private algorithms for counting under continual observation. Our main insight is that the matrix mechanism when using lower-triangular matrices can be used in the continual observation…
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed…
We describe a new approach to heavy-quark fragmentation which is based on a resummed perturbative calculation and parametrization of power corrections, concentrating on the z -> 1 limit, where the heavy meson carries a large fraction of the…
Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error…
This manuscript describes a technique for computing partial rank-revealing factorizations, such as, e.g, a partial QR factorization or a partial singular value decomposition. The method takes as input a tolerance $\varepsilon$ and an…
We investigate the stability of quantum Markov processes with respect to perturbations of their transition maps. In the first part, we introduce a condition number that measures the sensitivity of fixed points of a quantum channel to…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…