Block Householder transformation for parallel QR factorization

Rotella, Frédéric; Zambettakis, Irène

doi:10.1016/s0893-9659(99)00028-2

Cited by 28 publications

(11 citation statements)

References 3 publications

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“…To achieve this, let the matrix D = [a(θ 1 ), a(θ 2 ), ..., a(θ L )] contain the array response vectors that correspond to the L AoAs in Θ. Using Householder transformation [32], the orthogonal beam matrix Q ∈ C N ×N can be obtained as follows…”

Section: Antenna Fault Detection At the Receivermentioning

confidence: 99%

Millimeter-Wave Antenna Array Diagnosis with Partial Channel State Information

Medina

Jida

Pulipali

et al. 2021

ICC 2021 - IEEE International Conference on Communications

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Large antenna arrays enable directional precoding for Millimeter-Wave (mmWave) systems and provide sufficient link budget to combat the high path-loss at these frequencies. Due to atmospheric conditions and hardware malfunction, outdoor mmWave antenna arrays are prone to blockages or complete failures. This results in a modified array geometry, distorted far-field radiation pattern, and system performance degradation. Recent remote array diagnostic techniques have emerged as an effective way to detect defective antenna elements in an array with few diagnostic measurements. These techniques, however, require full and perfect channel state information (CSI), which can be challenging to acquire in the presence of antenna faults. This paper proposes a new remote array diagnosis technique that relaxes the need for full CSI and only requires knowledge of the incident angle-of-arrivals, i.e. partial channel knowledge. Numerical results demonstrate the effectiveness of the proposed technique and show that fault detection can be obtained with comparable number of diagnostic measurements required by diagnostic techniques based on full channel knowledge. In presence of channel estimation errors, the proposed technique is shown to out-perform recently proposed array diagnostic techniques.

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Section: Antenna Fault Detection At the Receivermentioning

confidence: 99%

Millimeter-Wave Antenna Array Diagnosis with Partial Channel State Information

Medina

Jida

Pulipali

et al. 2021

ICC 2021 - IEEE International Conference on Communications

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“…For use in intrinsically parallel environments like CFD, however, the Householder method requires significantly more message passing between processes. In parallel environments, Householder transformations are typically implemented using a block approach, where the Householder transformations are performed locally on each block of unknowns assigned to that process and then combined in a tree pattern 26,27 . Gram-Schmidt is significantly easier to implement and significantly faster for CFD applications if the loss of orthogonality can be tolerated.…”

Section: B Subspace Vector Orthogonalizationmentioning

confidence: 99%

“…! are of the form given in Eqn (27). The subscript on the block elements of A indicate the row in the matrix that the term appears in while the superscript is used to indicate the column that the term appears in, where indices not listed in the superscript are assumed to be !…”

Section: Linear System Preconditioningmentioning

confidence: 99%

Implementation of Generalized Minimum Residual Krylov Subspace Method for Chemically Reacting Flows

MacLean

White

2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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Two independent implementations of the Generalized Minimum Residual (GMRES)technique have been tested in the chemically reacting DPLR CFD code. The first implementation utilizes the existing Jacobian matrices by writing a new GMRES solver that is integrated directly into the DPLR CFD code time integration subroutine. The second implementation makes calls to the Portable, Extensible Toolkit for Scientific Computation (PETSc), an external linear and non-linear solver package, to perform the GMRES calculation. Several important aspects of developing the built-in GMRES solver are explored including basis vector orthogonalization technique, linear system pre-conditioning, parallelization, and convergence criteria. The resulting performance is compared with the PETSc implementation as well as line-and point-relaxation schemes for hypersonic cone, O /55 O double cone, and spherical capsule test cases. Overall, line-relaxation is typically the most efficient solution technique when elapsed time is measured, but GMRES is observed to provide more accurate solution of the matrices by measuring residual decrease per iteration. In the double cone test case at high enthalpy, the GMRES method is shown to be numerically more stable. Comparisons between PETSc and the built-in GMRES solversshow that choice of convergence criteria drive the relative performance of the solvers. Nomenclature A= sparse Jacobian matrix of target system b = right-hand side vector of target system c = Givens rotation cosine d = diagonal elements of ILU preconditioner, Eqn (29) e i,j = unit vector of length j, with one non-zero element, i E = lower off-diagonal elements of sparse A F = upper off-diagonal elements of sparse A G = Givens rotation matrix H = Hessenberg matrix k = number of line-relaxation steps L = lower diagonal matrix for Householder transformation, Eqn (9) m = number of GMRES relaxation steps M = dimension/rank of Krylov subspace N = dimension/rank of linear system P = preconditioner matrix p = order of ILU fill Q = matrix of orthogonal basis vectors r = residual R = transformed Hessenberg matrix s = Givens rotation sine u =

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“…In this work, we describe in detail the embedding of a single impurity in the one-dimensional (1D) Hubbard model. Note that a multiple-impurity version of the theory that would be applicable to any second-quantized Hamiltonian, by analogy with regular DMET, can be derived via a block-Householder transformation [54]. Work is currently in progress in this direction and will be presented in a separate paper.…”

Section: Introductionmentioning

confidence: 99%

Householder transformed density matrix functional embedding theory

Sekaran,

Tsuchiizu,

Saubanère

et al. 2021

Preprint

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Single-impurity quantum embedding based on the (one-electron reduced) density matrix is revisited by means of the unitary Householder transformation. While being exact and equivalent to (but formally simpler than) density matrix embedding theory (DMET) in the non-interacting case, the resulting Householder transformed density matrix functional embedding theory (Ht-DMFET) preserves, by construction, the single-particle character of the bath when electron correlation is introduced. In Ht-DMFET, the projected "impurity+bath" cluster's Hamiltonian (from which approximate properties of the interacting lattice can be extracted) becomes an explicit functional of the density matrix. In the spirit of DMET, we use in this work a closed (two-electron) cluster constructed from the full-size non-interacting density matrix. When the bath is interacting, per-site energies obtained for the half-filled one-dimensional Hubbard lattice match almost perfectly the exact Bethe Ansatz results in all correlation regimes. In the strongly correlated regime, the results deteriorate away from half-filling and no density-driven Mott-Hubbard transition is observed. These flaws originate from the fact that, in the exact theory, the Householder cluster is an open subsystem. Extending Ht-DMFET to multiple impurities via a block-Householder transformation is a natural follow-up to this work. Connections with density/density matrix functional theories should also be explored. Work is currently in progress in these directions.

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Block Householder transformation for parallel QR factorization

Cited by 28 publications

References 3 publications

Millimeter-Wave Antenna Array Diagnosis with Partial Channel State Information

Millimeter-Wave Antenna Array Diagnosis with Partial Channel State Information

Implementation of Generalized Minimum Residual Krylov Subspace Method for Chemically Reacting Flows

Householder transformed density matrix functional embedding theory

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