subject:(gauss newton algorithm)

University of Illinois – Chicago

1. Bliss, Nathan R. Computing Series Expansions of Algebraic Space Curves.

Degree: 2018, University of Illinois – Chicago

► We work towards a series-based computational approach for polynomial systems having positive-dimensional solution sets. The tropical variety gives information on the exponents of the leading… (more)

Subjects/Keywords: computational algebraic geometry; puiseux series; gauss-newton algorithm; tropical geometry; polynomial systems; homotopy continuation

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bliss, N. R. (2018). Computing Series Expansions of Algebraic Space Curves. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/22682

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Bliss, Nathan R. “Computing Series Expansions of Algebraic Space Curves.” 2018. Thesis, University of Illinois – Chicago. Accessed January 28, 2021. http://hdl.handle.net/10027/22682.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Bliss, Nathan R. “Computing Series Expansions of Algebraic Space Curves.” 2018. Web. 28 Jan 2021.

Vancouver:

Bliss NR. Computing Series Expansions of Algebraic Space Curves. [Internet] [Thesis]. University of Illinois – Chicago; 2018. [cited 2021 Jan 28]. Available from: http://hdl.handle.net/10027/22682.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bliss NR. Computing Series Expansions of Algebraic Space Curves. [Thesis]. University of Illinois – Chicago; 2018. Available from: http://hdl.handle.net/10027/22682

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

2. Morad, Farhad. Non-linear Curve Fitting.

Degree: Culture and Communication, 2019, Mälardalen University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-43600

►

The work done in this thesis is to examine various methods for curve fitting. Linear least squares and non-linear least squares will be described… (more)

Subjects/Keywords: Curve Fitting; Power-exponential function; Gauss-Newton algorithm; Levenberg-Marquardt algorithm; Linear and non-linear curve fitting; Kurvanpassning; Potens-exponential funktion; Gauss-Newton-algoritm; Levenberg-Marquardt-algoritm; Linjär och ickelinjär kurvanpassning; Other Mathematics; Annan matematik

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Morad, F. (2019). Non-linear Curve Fitting. (Thesis). Mälardalen University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-43600

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Morad, Farhad. “Non-linear Curve Fitting.” 2019. Thesis, Mälardalen University. Accessed January 28, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-43600.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Morad, Farhad. “Non-linear Curve Fitting.” 2019. Web. 28 Jan 2021.

Vancouver:

Morad F. Non-linear Curve Fitting. [Internet] [Thesis]. Mälardalen University; 2019. [cited 2021 Jan 28]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-43600.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Morad F. Non-linear Curve Fitting. [Thesis]. Mälardalen University; 2019. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-43600

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Indian Institute of Science

3. Gupta, Saurabh. Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography.

Degree: PhD, Faculty of Engineering, 2017, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2608

► Stable and computationally efficient reconstruction methodologies are developed to solve two important medical imaging problems which use near-infrared (NIR) light as the source of interrogation,… (more)

▼ Stable and computationally efficient reconstruction methodologies are developed to solve two important medical imaging problems which use near-infrared (NIR) light as the source of interrogation, namely, diffuse optical tomography (DOT) and one of its variations, ultrasound-modulated optical tomography (UMOT). Since in both these imaging modalities the system matrices are ill-conditioned owing to insufficient and noisy data, the emphasis in this work is to develop robust stochastic filtering algorithms which can handle measurement noise and also account for inaccuracies in forward models through an appropriate assignment of a process noise. However, we start with demonstration of speeding of a Gauss-Newton (GN) algorithm for DOT so that a video-rate reconstruction from data recorded on a CCD camera is rendered feasible. Towards this, a computationally efficient linear iterative scheme is proposed to invert the normal equation of a Gauss-Newton scheme in the context of recovery of absorption coefficient distribution from DOT data, which involved the singular value decomposition (SVD) of the Jacobian matrix appearing in the update equation. This has sufficiently speeded up the inversion that a video rate recovery of time evolving absorption coefficient distribution is demonstrated from experimental data. The SVD-based algorithm has made the number of operations in image reconstruction to be rather than. 2()ONN3()ONN The rest of the algorithms are based on different forms of stochastic filtering wherein we arrive at a mean-square estimate of the parameters through computing their joint probability distributions conditioned on the measurement up to the current instant. Under this, the first algorithm developed uses a Bootstrap particle filter which also uses a quasi-Newton direction within. Since keeping track of the Newton direction necessitates repetitive computation of the Jacobian, for all particle locations and for all time steps, to make the recovery computationally feasible, we devised a faster update of the Jacobian. It is demonstrated, through analytical reasoning and numerical simulations, that the proposed scheme, not only accelerates convergence but also yields substantially reduced sample variance in the estimates vis-à-vis the conventional BS filter. Both accelerated convergence and reduced sample variance in the estimates are demonstrated in DOT optical parameter recovery using simulated and experimental data. In the next demonstration a derivative free variant of the pseudo-dynamic ensemble Kalman filter (PD-EnKF) is developed for DOT wherein the size of the unknown parameter is reduced by representing of the inhomogeneities through simple geometrical shapes. Also the optical parameter fields within the inhomogeneities are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions). The EnKF is then used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The… Advisors/Committee Members: Vasu, Ram Mohan (advisor), Roy, Debasish (advisor).

Subjects/Keywords: Optical Tompgraphy; Diffuse Optical Tomography (DOT); Ultrasound Modulated Optical Tomography (UMOT); Inverse Problems; Gauss-Newton Algorithm; Pseuo-Dynamic Ensemble Kalman Filter; Stochastic Algorithms; Stochastic Filtering Algorithms; Medical Imaging; Medical Instrumentation

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gupta, S. (2017). Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2608

Chicago Manual of Style (16^th Edition):

Gupta, Saurabh. “Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography.” 2017. Doctoral Dissertation, Indian Institute of Science. Accessed January 28, 2021. http://etd.iisc.ac.in/handle/2005/2608.

MLA Handbook (7^th Edition):

Gupta, Saurabh. “Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography.” 2017. Web. 28 Jan 2021.

Vancouver:

Gupta S. Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2017. [cited 2021 Jan 28]. Available from: http://etd.iisc.ac.in/handle/2005/2608.

Council of Science Editors:

Gupta S. Development Of Deterministic And Stochastic Algorithms For Inverse Problems Of Optical Tomography. [Doctoral Dissertation]. Indian Institute of Science; 2017. Available from: http://etd.iisc.ac.in/handle/2005/2608

4. Altoumaimi, Rasha Talal. Nonlinear Least-Square Curve Fitting of Power-Exponential Functions: Description and comparison of different fitting methods.

Degree: Culture and Communication, 2017, Mälardalen University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-38606

► This thesis examines how to find the best fit to a series of data points when curve fitting using power-exponential models. We describe the… (more)

Subjects/Keywords: Curve ﬁtting; Power exponential functions; Gauss-Newton algorithms; Levenberg Marquardt algorithm; death rate; rocket-triggered lightning return strokes; Natural Sciences; Naturvetenskap; Mathematics; Matematik

…the Gauss-Newton algorithm and the Levenberg-Marquardt algorithm . 47 5.3 5.4 5.5 5… …sizes as one step results in convergence. Algorithm 2. Gauss-Newton Method • Step 0: Choose an… …generated by the Gauss-Newton algorithm converges to b∗ for all b0 ∈ D ≡ {b| k b − b∗ k< ε… …starting parameters, this algorithm usually a little of less speed than the Gauss-Newton one… …methods of analysis and standards in performance when fitting models to data: Gauss-Newton…

10 more images…

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Altoumaimi, R. T. (2017). Nonlinear Least-Square Curve Fitting of Power-Exponential Functions: Description and comparison of different fitting methods. (Thesis). Mälardalen University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-38606

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Altoumaimi, Rasha Talal. “Nonlinear Least-Square Curve Fitting of Power-Exponential Functions: Description and comparison of different fitting methods.” 2017. Thesis, Mälardalen University. Accessed January 28, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-38606.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Altoumaimi, Rasha Talal. “Nonlinear Least-Square Curve Fitting of Power-Exponential Functions: Description and comparison of different fitting methods.” 2017. Web. 28 Jan 2021.

Vancouver:

Altoumaimi RT. Nonlinear Least-Square Curve Fitting of Power-Exponential Functions: Description and comparison of different fitting methods. [Internet] [Thesis]. Mälardalen University; 2017. [cited 2021 Jan 28]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-38606.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Altoumaimi RT. Nonlinear Least-Square Curve Fitting of Power-Exponential Functions: Description and comparison of different fitting methods. [Thesis]. Mälardalen University; 2017. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-38606

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Open Access Theses and Dissertations