Continuation method for a right definite two-parameter eigenvalue problem

被引:19
|
作者
Plestenjak, B [1 ]
机构
[1] Univ Ljubljana, IMFM TCS, SI-1000 Ljubljana, Slovenia
关键词
right deffinite two parameter problem; continuation method; Newton's method; Rayleigh quotient iteration;
D O I
10.1137/S0895479898346193
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The continuation method has been successfully applied to the classical Ax = lambda x and to the generalized Ax = lambda Bx eigenvalue problems. Shimasaki applied the continuation method to the right definite two-parameter problem, which resulted in a discretization of a two-parameter Sturm-Liouville problem. We show that the continuation method can be used for a general right definite two-parameter problem and we give a sketch of the algorithm. For a local convergent method we use the tensor Rayleigh quotient iteration (TRQI), which is a generalization of the Rayleigh iterative method to two-parameter problems. We show its convergence and compare it with Newton's method and with the generalized Rayleigh quotient iteration (GRQI), studied by Ji, Jiang, and Lee.
引用
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页码:1163 / 1184
页数:22
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