A modified iterative refinement algorithm for efficient solution of parameter-dependent sets of linear equations

2002 ◽  
Author(s):  
P.S. Simon ◽  
C.S. Kenney ◽  
K. McInturff ◽  
R.W. Jobsky ◽  
T.A. Bryan
Keyword(s):  
Efficient Solution ◽  
Linear Equations ◽  
Iterative Refinement ◽  
Parameter Dependent ◽  
Refinement Algorithm

New Research Results of Algorithms for Analysis of Changing Electric Circuits

2020 ◽  
Vol 63 (6) ◽  
pp. 29-36
Author(s):  
Ivan Lebedev ◽  
◽  
Nikolai Savelov ◽  
Keyword(s):  
Numerical Experiments ◽  
Linear Equations ◽  
Iterative Refinement ◽  
Floating Point ◽  
Electrical Circuits ◽  
Electric Circuits ◽  
Research Results ◽  
Systems Of Linear Equations ◽  
New Research ◽  
Refinement Algorithm

New research results in the field of accelerated analysis of linear and linearizable electrical circuits with variable elements are presented. The considered algorithms are based on a new modification of Gaussian elim-ination for solution of systems of linear equations. The researches was directed on a systematic thorough study of the phenomenon of quasi-stabilization of the error discovered by the authors during multiple repeated cir-cuit analyzes. The Sherman-Morrison algorithm and the iterative refinement algorithm are considered as alter-natives. To control the results of numerical experiments, the representation of floating-point numbers in the bi-nary128 format of the IEEE 754 standard is used. A method for the machine formation of mathematical models of circuits with an unlimited number of elements is proposed.

Double shear layer evolution on the non-uniform computational mesh

2021 ◽  
Author(s):  
Yu M. Kulikov ◽  
E. E. Son
Keyword(s):  
Shear Layer ◽  
Iterative Refinement ◽  
The Novel ◽  
Original Sequence ◽  
Double Shear ◽  
Computational Mesh ◽  
Mesh Resolution ◽  
Initial Vorticity ◽  
High Resolution Technique ◽  
Refinement Algorithm

Abstract This paper considers the canonical problem of a thin shear layer evolution at Reynolds number Re = 400000 using the novel Compact Accurately Boundary Adjusting high-Resolution Technique (CABARET). The study is focused on the effect of the specific mesh refinement in the high shear rate areas on the flow properties under the influence of the developing instability. The original sequence of computational meshes (256^2, 512^2, 1024^2, 2048^2 cells) is modified using an iterative refinement algorithm based on the hyperbolic tangent. The properties of the solutions obtained are discussed in terms of the initial momentum thickness and the initial vorticity thickness, viscous and dilatational dissipation rates and also integral enstrophy. The growth rate for the most unstable mode depending on the mesh resolution is considered. In conclusion the accuracy of calculated mesh functions is estimated via L1, L2, L∞ norms.

An Iterative Refinement Algorithm for the Minimum Branch Vertices Problem

2011 ◽  
pp. 421-433 ◽  
Author(s):  
Diego M. Silva ◽  
Ricardo M. A. Silva ◽  
Geraldo R. Mateus ◽  
José F. Gonçalves ◽  
Mauricio G. C. Resende ◽  
...  
Keyword(s):  
Iterative Refinement ◽  
Refinement Algorithm

Research on the Repeater Optimization Based on Voronoi Model

2012 ◽  
Vol 588-589 ◽  
pp. 802-805
Author(s):  
Ban Teng Liu ◽  
Xi Lin Hu ◽  
Zheng Yu Xu ◽  
Yao Lin Liu ◽  
You Rong Chen
Keyword(s):  
Cellular Networks ◽  
Voronoi Diagram ◽  
Iterative Refinement ◽  
Local Optimum ◽  
Limited Capacity ◽  
Circular Area ◽  
Absolute Minimum ◽  
Voronoi Regions ◽  
Refinement Algorithm ◽  
Better Than

This paper propose a two-tiered network in which lower-power users communicate with one another through repeaters, which amplify signals and retransmit them, have limited capacity, and may interfere with one another if their transmitter frequencies are close and they share the same private-line tone. Motivated by cellular networks, this paper gives a naive solution where the number of repeaters and their positions can be obtained analytically. In a circular area with radius 40 miles, 12 repeaters can accommodate 1,000 simultaneous users. This paper further propose an iterative refinement algorithm consisting of three fundamental modules that draw the Voronoi diagram, determine the centers of the circumscribed circles of the Voronoi regions, and escape the local optimum by using external optimization. The algorithm obtains a solution with 11 repeaters, which we prove to be the absolute minimum. For 10,000 users, it uses 104 repeaters, better than the naive solution's 108.

scholarly journals ACCURATE OPTICAL TARGET POSE DETERMINATION FOR APPLICATIONS IN AERIAL PHOTOGRAMMETRY

2016 ◽  
Vol III-3 ◽  
pp. 257-262 ◽  
Author(s):  
D. A. Cucci
Keyword(s):  
Target Position ◽  
Iterative Refinement ◽  
Target Size ◽  
Geometric Invariant ◽  
Pose Determination ◽  
Aerial Photogrammetry ◽  
Circle Center ◽  
Position And Orientation ◽  
Orientation Determination ◽  
Refinement Algorithm

We propose a new design for an optical coded target based on concentric circles and a position and orientation determination algorithm optimized for high distances compared to the target size. If two ellipses are fitted on the edge pixels corresponding to the outer and inner circles, quasi-analytical methods are known to obtain the coordinates of the projection of the circles center. We show the limits of these methods for quasi-frontal target orientations and in presence of noise and we propose an iterative refinement algorithm based on a geometric invariant. Next, we introduce a closed form, computationally inexpensive, solution to obtain the target position and orientation given the projected circle center and the parameters of the outer circle projection. The viability of the approach is demonstrated based on aerial pictures taken by an UAV from elevations between 10 to 100 m. We obtain a distance RMS below 0.25 % under 50 m and below 1 % under 100 m with a target size of 90 cm, part of which is a deterministic bias introduced by image exposure.

scholarly journals ACCURATE OPTICAL TARGET POSE DETERMINATION FOR APPLICATIONS IN AERIAL PHOTOGRAMMETRY

2016 ◽  
Vol III-3 ◽  
pp. 257-262 ◽  
Author(s):  
D. A. Cucci
Keyword(s):  
Target Position ◽  
Iterative Refinement ◽  
Target Size ◽  
Geometric Invariant ◽  
Pose Determination ◽  
Aerial Photogrammetry ◽  
Circle Center ◽  
Position And Orientation ◽  
Orientation Determination ◽  
Refinement Algorithm

We propose a new design for an optical coded target based on concentric circles and a position and orientation determination algorithm optimized for high distances compared to the target size. If two ellipses are fitted on the edge pixels corresponding to the outer and inner circles, quasi-analytical methods are known to obtain the coordinates of the projection of the circles center. We show the limits of these methods for quasi-frontal target orientations and in presence of noise and we propose an iterative refinement algorithm based on a geometric invariant. Next, we introduce a closed form, computationally inexpensive, solution to obtain the target position and orientation given the projected circle center and the parameters of the outer circle projection. The viability of the approach is demonstrated based on aerial pictures taken by an UAV from elevations between 10 to 100 m. We obtain a distance RMS below 0.25 % under 50 m and below 1 % under 100 m with a target size of 90 cm, part of which is a deterministic bias introduced by image exposure.

ACCUMULATION OF THE CHOLESKY SQUARE ROOT IN HELMERT BLOCKING

1986 ◽  
Vol 40 (3) ◽  
pp. 297-314
Author(s):  
D. R. Junkins ◽  
R. R. Steeves
Keyword(s):  
Efficient Solution ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Computational Method ◽  
Normal Equation ◽  
Square Root ◽  
Unknown Parameters ◽  
Normal Equations ◽  
Systems Of Linear Equations ◽  
Large Systems

The Helmert blocking method is being used in the present effort to readjust North American geodetic networks. Combining this method with the Cholesky computational method enables the efficient solution of very large systems of linear equations. A by-product of this approach is a “partial” Cholesky square root for each Helmert block. This paper demonstrates that the Cholesky square root for the entire system of normal equations can be constructed from partial Cholesky square root blocks that are produced during the Helmert block adjustment, even though various reorderings of the unknown parameters are necessary throughout the computations. The entire Cholesky square root can be used to compute the inverse of the normal equation coefficient matrix, which is needed for post-adjustment statistical analyses.

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