Deflation techniques for the calculation of further solutions of a nonlinear system

Brow, Kenneth M.; Gearhart, W. B.

doi:10.1007/bf02165004

Cited by 76 publications

(52 citation statements)

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“…Figure 2 shows that 2 = |x (2) − r (1) | < δ, hence, p( 2 ) < 1 and p(|x (2) − r (1) |)w (x (2) ) < w (x (2) ). Consequently, in order to perform the third iteration, at x (2) we do not use the tangent but the straight line having the slope smaller than w (x (2) ), leading to x (3) as illustrated in Fig. 2.…”

Section: Finding Multiple DC Operating Pointsmentioning

confidence: 99%

“…The approach proposed in this paper employs a concept known in mathematics under the name deflation [3,9]. The main idea of deflation is as follows.…”

mentioning

confidence: 99%

“…In Ref. [3] the following deformation is proposed. Let M(x, r (1) ) be an n × n matrix, called a deflation matrix, such that…”

mentioning

confidence: 99%

“…Certainly, r (1) is not a solution of this equation and the sequence generated by the method will converge to other solution. A simple deflation matrix [3] is…”

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confidence: 99%

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A Method for Finding Multiple DC Operating Points of Short Channel CMOS Circuits

Tadeusiewicz

Hałgas

2013

Circuits Syst Signal Process

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This paper is devoted to the analysis of CMOS transistor circuits, fabricated in nanometer technology, having multiple DC operating points. The MOS transistors are characterised by the intricate PSP 103.1.1 model elected by the CMC as a standard. To find the operating points an approach is proposed based on a mathematical concept called a deflation. According to this concept the equations describing the circuit are deformed to avoid the solutions earlier determined and retain the remaining solutions. A new efficient deflation technique is developed and combined with the homotopy method and the discrete circuit equivalent of the Newton-Raphson nodal analysis. An algorithm has been worked out for finding multiple DC operating points of CMOS circuits encountered in practical applications. To illustrate the proposed approach three numerical examples are given.

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Section: Finding Multiple DC Operating Pointsmentioning

confidence: 99%

“…The approach proposed in this paper employs a concept known in mathematics under the name deflation [3,9]. The main idea of deflation is as follows.…”

mentioning

confidence: 99%

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A Method for Finding Multiple DC Operating Points of Short Channel CMOS Circuits

Tadeusiewicz

Hałgas

2013

Circuits Syst Signal Process

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“…The importance of the problem has attracted the attention of many research efforts and, as a result, many different approaches to the problem exist. We briefly mention here the deflation techniques used for the calculation of further solutions [7] or other more efficient and more recent interval analysis based methods (see, e.g., [15,16,26,28,30,37]) and the methods described in [20,21,41]. The corresponding existence tool of interval analysis based methods is the availability of the range of the function in a given interval, which can be implemented using interval arithmetic, though range overestimation, and hence efficiency problems must be resolved.…”

Section: Isolating the Roots Of A Univariate Polynomialmentioning

confidence: 99%

On the Complexity of Isolating Real Roots and Computing with Certainty the Topological Degree

Mourrain

Vrahatis

Yakoubsohn

2002

Journal of Complexity

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In this contribution the isolation of real roots and the computation of the topological degree in two dimensions are considered and their complexity is analyzed. In particular, we apply Stenger's degree computational method by splitting properly the boundary of the given region to obtain a sequence of subintervals along the boundary that forms a sufficient refinement. To this end, we properly approximate the function using univariate polynomials. Then we isolate each one of the zeros of these polynomials on the boundary of the given region in various subintervals so that these subintervals form a sufficiently refined boundary. © 2002 Elsevier Science (USA)

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Benchmarking a Single‐Objective Optimization Test Bed for Parametric Study on Differential Evolution

Qing

2009

Differential Evolution

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The parametric study on differential evolution must be carried out on a test bed. When the parametric study was initiated in 2004, the initial test bed only included the benchmark electromagnetic inverse scattering problem and two toy functions defined by this author. As such it was seriously inadequate from the point of view of problem features. The features of an application problem may affect the choice of strategy, intrinsic and non-intrinsic control parameters. The relationship between problem features, strategy, intrinsic and non-intrinsic control parameters is of great significance. It is therefore necessary to build a test bed with all representative problem features fully and appropriately addressed.Although many test beds are available, none of them is satisfactory. No effort to benchmark a test bed for unconstrained single-objective optimization has been found with problem features fully and properly addressed. When evaluating an evolutionary algorithm, people usually choose test problems from the available literature. Very often, insufficient attention is given to problem features. A Survey on Test Problems SourcesThere are two sources for test problems. Optimization publications including books, journals, conference proceedings, technical reports, degree thesis, and so on, contain numerous test problems. In general, test problems from this source are more trustworthy because of the careful reviewing and proofreading that precede publication. However, using this source is very tedious and time-consuming. Moreover, access to optimization publications is usually limited.

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Deflation techniques for the calculation of further solutions of a nonlinear system

Cited by 76 publications

References 1 publication

A Method for Finding Multiple DC Operating Points of Short Channel CMOS Circuits

A Method for Finding Multiple DC Operating Points of Short Channel CMOS Circuits

On the Complexity of Isolating Real Roots and Computing with Certainty the Topological Degree

Benchmarking a Single‐Objective Optimization Test Bed for Parametric Study on Differential Evolution

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