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The Bayesian Reconstruction (BR) Method

Alexander Rothkopf


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<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
  <dc:creator>Alexander Rothkopf</dc:creator>
  <dc:date>2021-07-14</dc:date>
  <dc:description>//*********************************************************************************
//
//    Bayesian Spectral Reconstruction and Extended MEM
//
//    Code: Dr. Alexander Karl Rothkopf               DATE: July 14th 2021
//
//    Method: Dr. Yannis Burnier, Dr. Alexander Karl Rothkopf DATE: 2013
//    ========================================================================
//
//    THIS PROGRAM IS AN IMPLEMENTATION OF TWO BAYESIAN APPROACHES
//    FOR THE NUMERICAL INVERSION OF THE TYPICALLY ILL DEFINED TASK
//
//    DATA[t] = Int_-WMIN^WMAX [ K[w,t] * SPEC[w] ]dw
//
//    WHERE THE GOAL IS TO EXTRACT THE SPECTRAL FUNCTION SPEC[w] FROM
//    THE PROVIDED LATTICE DATA DATA[t] USING A PREVIOUSLY SPECIFIED
//    KERNEL FUNCTION K[w,t].
//
//    References:
//
//    Y. Burnier and A. Rothkopf,
//    "Bayesian Approach to Spectral Function Reconstruction for
//     Euclidean Quantum Field Theories"
//    arXiv:1307.6106 [hep-lat]
//    Phys. Rev. Lett. 111, 182003 (2013)
//
//    A. Rothkopf
//    "Improved Maximum Entropy Analysis with an Extended Search Space"
//    arXiv:1110.6285 [physics.comp-ph]
//    J.Comput.Phys. 238 (2013) 106-114
//
//*********************************************************************************

//*********************************************************************************
//    This program uses adapted code from two libraries:
//
//    1. The GNU Scientific Library:
//
//        SINGULAR VALUE DECOMPOSITION
//        EIGENSYSTEMS OF SYMMETRIC MATRICES
//        MATRIX INVERSION BASED ON QR DECOMPOSITION
//        SOLVER FOR Ax=b BASED ON QR DECOMPOSITION
//
//    2. The ALGLIB Library (MPFR part 2.6.):
//
//        LBFGS MINIMIZER
//        LEVENBERG MARQUARD + LBFGS PRECONDITIONER MINIMIZER
//        EIGENVALUES FOR NON_SYMMETRIC MATRICES
//
//*********************************************************************************

 </dc:description>
  <dc:identifier>https://zenodo.org/record/5102934</dc:identifier>
  <dc:identifier>10.5281/zenodo.5102934</dc:identifier>
  <dc:identifier>oai:zenodo.org:5102934</dc:identifier>
  <dc:relation>doi:10.5281/zenodo.5102933</dc:relation>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:rights>https://creativecommons.org/licenses/by/4.0/legalcode</dc:rights>
  <dc:subject>Bayesian inference, spectral reconstruction, spectral function, inverse problem, BR Method, Maximum Entropy Method,</dc:subject>
  <dc:title>The Bayesian Reconstruction (BR) Method</dc:title>
  <dc:type>info:eu-repo/semantics/other</dc:type>
  <dc:type>software</dc:type>
</oai_dc:dc>
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