A fixed-point homotopy method for solving modified nodal equations

Yamamura, Kenichiro; Sekiguchi, Tooru; Inoue, Y.

doi:10.1109/81.768822

Cited by 69 publications

(23 citation statements)

References 21 publications

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“…The MATLAB results listed in Table II are comparable with solutions from other homotopy implementations [70]. Even though Newton-Raphson method solvers implemented in simulators such as SPICE 3 [45], SPICE 3F5 [44], and PSPICE [42] will calculate only one dc operating point, it is possible to provide PSPICE with an initial guess that is close to a desired solution by using the .NODESET option.…”

Section: Four-transistor Circuitmentioning

confidence: 75%

“…Various homotopy algorithms have been introduced for finding multiple solutions of nonlinear circuit equations [4,40] and for finding dc operating points of transistor circuits [16,24,28,43,56,58,68]. Homotopy algorithms were implemented in a number of developed stand-alone circuit simulators [69,70], simulators developed based on SPICE [55,58], and proprietary industrial tools designed for simulation of analog circuits such as ADVICE at AT&T [12,34,51,52] and TITAN at Siemens [33]. They have been successful in finding solutions to highly nonlinear circuits that could not be simulated using conventional numerical methods.…”

Section: Parameter Embedding and Continuation Methodsmentioning

confidence: 99%

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DC operating points of transistor circuits

Trajković

2012

NOLTA

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Abstract:Finding a circuit's dc operating points is an essential step in its design and involves solving systems of nonlinear algebraic equations. Of particular research and practical interests are dc analysis and simulation of electronic circuits consisting of bipolar junction and fieldeffect transistors (BJTs and FETs), which are building blocks of modern electronic circuits. In this paper, we survey main theoretical results related to dc operating points of transistor circuits and discuss numerical methods for their calculation.

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Section: Four-transistor Circuitmentioning

confidence: 75%

Section: Parameter Embedding and Continuation Methodsmentioning

confidence: 99%

DC operating points of transistor circuits

Trajković

2012

NOLTA

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“…The homotopy methods have been proposed to efficiently find out the multiple solutions for the nonlinear algebraic equations. Furthermore, homotopy methods which have globally convergent property, are well-known in the field of circuit simulation [43,44]. Homotopy methods define mappings from the given problem for which the solution is desired, and these mappings define "paths" to the desired solution.…”

Section: Analytical Methods To Improve Learning Convergencementioning

confidence: 99%

Development of Advanced Verification and Validation Procedures and Tools for the Certification of Learning Systems in Aerospace Applications

et al. 2005

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Adaptive control technologies that incorporate learning algorithms have been proposed to enable automatic flight control and vehicle recovery, autonomous flight, and to maintain vehicle performance in the face of unknown, changing, or poorly defined operating environments. In order for adaptive control systems to be used in safety-critical aerospace applications, they must be proven to be highly safe and reliable. Rigorous methods for adaptive software verification and validation must be developed to ensure that control system software failures will not occur. Of central importance in this regard is the need to establish reliable methods that guarantee convergent learning, rapid convergence (learning) rate, and algorithm stability. This paper presents the major problems of adaptive control systems that use learning to improve performance. The paper then presents the major procedures and tools presently developed or currently being developed to enable the verification, validation, and ultimate certification of these adaptive control systems. These technologies include the application of automated program analysis methods, techniques to improve the learning process, analytical methods to verify stability, methods to automatically synthesize code, simulation and test methods, and tools to provide on-line software assurance.

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“…In general, this method involves incorporating the continuation parameter into a set of nonlinear equations H (x, λ), where H : R n+1 → R n [4][5][6][7]. The computational efficiency of homotopy methods depends on the homotopy formulation as well as the curve-tracing algorithm and the initial point [4,5,[7][8][9][10][11]. The usefulness of homotopy methods depends on the type of a circuits descriptive equations.…”

Section: Introductionmentioning

confidence: 99%

Spherical Continuation Algorithm with Spheres of Variable Radius to Trace Homotopy Curves

Torres-Muñoz

Hernandez-Martinez

Vázquez-Leal

2015

Int. J. Appl. Comput. Math

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The homotopy continuation methods are capable to locate multiple solutions of nonlinear systems of equations. In this paper is presented the path-following technique used to trace the homotopy trajectory. The spherical method is employed resizing the radius of the sphere at each iteration, the above based on the behavior of the radius of curvature. Also the Newton homotopy is applied in conjunction with the proposed methodology for tracing homotopy curve. To prove the usefulness of the proposed method is applied to three examples with different numbers of equations obtaining successful results.

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A fixed-point homotopy method for solving modified nodal equations

Cited by 69 publications

References 21 publications

DC operating points of transistor circuits

DC operating points of transistor circuits

Development of Advanced Verification and Validation Procedures and Tools for the Certification of Learning Systems in Aerospace Applications

Spherical Continuation Algorithm with Spheres of Variable Radius to Trace Homotopy Curves

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