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ALESQ, a Nonlinear Least-Squares Fit Code, and TSOLVE, a Nonlinear Best Approximation Code, Third Edition
Tatsuo Tabata and Rinsuke Ito,
Institute for Data Evaluation and Analysis Technical Report Supplement (IDEA-TRS) No. 1
September 23, 2022
We describe algorithms for nonlinear least-squares fit and best approximation, which we made and used for many years. The basis of the least-squares fit algorithm is the maximum neighborhood algorithm developed by Levenberg and Marquardt, and we incorporated an improved strategy into it. We call the code for this algorithm ALESQ. For fitting the equation to the data with approximately equal relative uncertainties, we devised a two-step method and included conveniences for this method in ALESQ. We made the algorithm for the best approximation based on the one developed by Osborne and Watson, incorporating a procedure to solve the “continuous” best approximation problem with a discrete data set. The name of the code for this algorithm is TSOLVE. We included in TSOLVE a routine to estimate tolerances for the roundoff of the solution. Both ALESQ and TSOLVE are also applicable to linear problems. In Appendix A, we describe procedures and methods to formulate empirical equations. Appendix B lists the works for which we used ALESQ and TSOLVE. Those works are mainly of radiation and atomic collision physics. Appendix C and D contain FORTRAN codes of ALESQ and TSOLVE, respectively.
T Tabata,
Institute for Scientific and Artistic Cultures Technical Reports (ISAAC-TR) No. 1
March 26, 2021
Kamefuchi wrote an essay about Heisenberg’s and Yukawa’s tragic incidents in their later years. We have studied facts related to these incidents by looking up other references and found that Kamefuchi’s suppositions at three minor points about Heisenberg’s case are wrong. We have reviewed the literature evaluating the studies of the above two physicists in those years. The result has revealed that Heisenberg’s work influenced Nambu for finding spontaneous symmetry breaking in subatomic physics. On the other hand, Yukawa’s work has not had much impact on other researchers. We have also compared Kamefuchi’s classification of research methods of theoretical physics with Nambu’s two versions. The descending type method defined by Kamefuchi gives a convincing reason for the two physicists’ failures in finishing the later studies. To remove faults in Nambu’s revised version, we propose a new, two-aspect scheme, which indicates that the esthetic, bottom-up mode kept by Nambu made him a long-time productive theorist. In Appendix B, we describe Kamefuchi’s classification of theoretical physicists given in another essay and suggest a possible extension of our proposal.
T Tabata,
Institute for Data Evaluation and Analysis Technical Reports (IDEA-TR) No. 24
January 27, 2019; Last Modified June 7, 2019
The present volume contains two papers, published by Tatsuo Tabata and his coworkers in 2000 and 2007, in the form of the post-print re-edited by the use of LATEX. Tabata made these studies at Osaka Prefecture University and Institute for Data Evaluation and Analysis. The works belong to the category of psychology and treat the perception of mirror images (the so-called mirror puzzle). A “Commentary” section written by the editor is attached to the end of each paper.
Note: At the end of this volume, you can find the table of contents of all the volumes of Collected Works.