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過去の記録 ～04/25｜次回の予定｜今後の予定 04/26～
2009年01月09日(金)
16:00-17:00 数理科学研究科棟(駒場) 370号室
Leevan Ling 氏 (Hong Kong Baptist University)
Effective Condition Numbers and Laplace Equations
Leevan Ling 氏 (Hong Kong Baptist University)
Effective Condition Numbers and Laplace Equations
[ 講演概要 ]
The condition number of a matrix is commonly used for investigating the stability of solutions to linear algebraic systems. Recent meshless techniques for solving PDEs have been known to give rise to ill-conditioned matrices, yet are still able to produce results that are close to machine accuracy. In this work, we consider the method of fundamental solutions (MFS), which is known to solve, with extremely high accuracy, certain partial differential equations, namely those for which a fundamental solution is known. To investigate the applicability of the MFS, either when the boundary is not analytic or when the boundary data is not harmonic, we examine the relationship between its accuracy and the effective condition number.
The condition number of a matrix is commonly used for investigating the stability of solutions to linear algebraic systems. Recent meshless techniques for solving PDEs have been known to give rise to ill-conditioned matrices, yet are still able to produce results that are close to machine accuracy. In this work, we consider the method of fundamental solutions (MFS), which is known to solve, with extremely high accuracy, certain partial differential equations, namely those for which a fundamental solution is known. To investigate the applicability of the MFS, either when the boundary is not analytic or when the boundary data is not harmonic, we examine the relationship between its accuracy and the effective condition number.
