外推法
数学
厄米矩阵
基质(化学分析)
双线性插值
期限(时间)
正定矩阵
产品(数学)
价值(数学)
双线性形式
应用数学
组合数学
纯数学
数学分析
统计
特征向量
几何学
物理
量子力学
复合材料
材料科学
作者
Paraskevi Fika,Marilena Mitrouli
标识
DOI:10.1016/j.laa.2015.08.033
摘要
For a Hermitian matrix A∈Cp×p, given vectors x, y∈Cp and for suitable functions f, the bilinear form y⁎f(A)x is estimated by extending the extrapolation method proposed by C. Brezinski in 1999. Families of one term and two term estimates ef,ν, ν∈C and eˆf,n,k, n,k∈Z, respectively, are derived by extrapolation of the moments of the matrix A. For the positive definite case, bounds for the optimal value of ν, which leads to an efficient one term estimate in only one matrix vector product, are derived. For f(A)=A−1, a formula approximating this optimal value of ν is specified. Numerical results for several matrix functions and comparisons are provided to demonstrate the effectiveness of the extrapolation method.
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