The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Kaedah Jacobi-Davidson dan kaedah Riccati untuk masalah nilai eigen dikaji. Dalam kaedah, seseorang perlu menyelesaikan persamaan tak linear yang dipanggil persamaan pembetulan setiap lelaran, dan perbezaan antara kaedah datang dari cara menyelesaikan persamaan. Dalam kaedah Jacobi-Davidson/Riccati persamaan pembetulan diselesaikan dengan/tanpa linearisasi. Dalam literatur, mengelakkan linearisasi dikenali sebagai penambahbaikan untuk mendapatkan penyelesaian persamaan yang lebih baik dan membawa penumpuan yang lebih cepat. Malah, kaedah Riccati menunjukkan tingkah laku penumpuan yang unggul untuk beberapa masalah. Namun begitu kelebihan kaedah Riccati masih tidak jelas, kerana persamaan pembetulan diselesaikan bukan dengan tepat tetapi dengan ketepatan yang rendah. Dalam kertas ini, kami menganalisis penyelesaian anggaran persamaan pembetulan dan menjelaskan perkara bahawa kaedah Riccati dikhususkan untuk mengira penyelesaian tertentu masalah nilai eigen. Hasilnya menunjukkan bahawa kedua-dua kaedah harus digunakan secara selektif bergantung pada penyelesaian sasaran. Analisis kami telah disahkan oleh eksperimen berangka.
Takafumi MIYATA
Fukuoka Institute of Technology
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Salinan
Takafumi MIYATA, "On Correction-Based Iterative Methods for Eigenvalue Problems" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 10, pp. 1668-1675, October 2018, doi: 10.1587/transfun.E101.A.1668.
Abstract: The Jacobi-Davidson method and the Riccati method for eigenvalue problems are studied. In the methods, one has to solve a nonlinear equation called the correction equation per iteration, and the difference between the methods comes from how to solve the equation. In the Jacobi-Davidson/Riccati method the correction equation is solved with/without linearization. In the literature, avoiding the linearization is known as an improvement to get a better solution of the equation and bring the faster convergence. In fact, the Riccati method showed superior convergence behavior for some problems. Nevertheless the advantage of the Riccati method is still unclear, because the correction equation is solved not exactly but with low accuracy. In this paper, we analyzed the approximate solution of the correction equation and clarified the point that the Riccati method is specialized for computing particular solutions of eigenvalue problems. The result suggests that the two methods should be selectively used depending on target solutions. Our analysis was verified by numerical experiments.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.1668/_p
Salinan
@ARTICLE{e101-a_10_1668,
author={Takafumi MIYATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On Correction-Based Iterative Methods for Eigenvalue Problems},
year={2018},
volume={E101-A},
number={10},
pages={1668-1675},
abstract={The Jacobi-Davidson method and the Riccati method for eigenvalue problems are studied. In the methods, one has to solve a nonlinear equation called the correction equation per iteration, and the difference between the methods comes from how to solve the equation. In the Jacobi-Davidson/Riccati method the correction equation is solved with/without linearization. In the literature, avoiding the linearization is known as an improvement to get a better solution of the equation and bring the faster convergence. In fact, the Riccati method showed superior convergence behavior for some problems. Nevertheless the advantage of the Riccati method is still unclear, because the correction equation is solved not exactly but with low accuracy. In this paper, we analyzed the approximate solution of the correction equation and clarified the point that the Riccati method is specialized for computing particular solutions of eigenvalue problems. The result suggests that the two methods should be selectively used depending on target solutions. Our analysis was verified by numerical experiments.},
keywords={},
doi={10.1587/transfun.E101.A.1668},
ISSN={1745-1337},
month={October},}
Salinan
TY - JOUR
TI - On Correction-Based Iterative Methods for Eigenvalue Problems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1668
EP - 1675
AU - Takafumi MIYATA
PY - 2018
DO - 10.1587/transfun.E101.A.1668
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2018
AB - The Jacobi-Davidson method and the Riccati method for eigenvalue problems are studied. In the methods, one has to solve a nonlinear equation called the correction equation per iteration, and the difference between the methods comes from how to solve the equation. In the Jacobi-Davidson/Riccati method the correction equation is solved with/without linearization. In the literature, avoiding the linearization is known as an improvement to get a better solution of the equation and bring the faster convergence. In fact, the Riccati method showed superior convergence behavior for some problems. Nevertheless the advantage of the Riccati method is still unclear, because the correction equation is solved not exactly but with low accuracy. In this paper, we analyzed the approximate solution of the correction equation and clarified the point that the Riccati method is specialized for computing particular solutions of eigenvalue problems. The result suggests that the two methods should be selectively used depending on target solutions. Our analysis was verified by numerical experiments.
ER -