## 5 Citations

Twenty years of asymptotic correction for eigenvalue computation

- Mathematics
- 2000

Asymptotic correction, first studied systematically in the 1979 ANU thesis of John Paine, can significantly increase the accuracy and efficiency of finite difference and finite element methods for…

Computation of mixed partial derivatives of eigenvalues and eigenvectors by simultaneous iteration

- Mathematics
- 1999

A new simultaneous iteration method is presented for computing mixed second-order partial derivatives of several eigenvalues and the corresponding eigenvectors of a matrix which depends smoothly on…

Methods for solving underdetermined systems

- Computer ScienceNumer. Linear Algebra Appl.
- 2018

Some alternative methods for computing solutions of underdetermined linear systems, Ax=b, with implications for computing eigenvector derivatives and make some recommendations are compared.

Broyden method for inverse non-symmetric Sturm-Liouville problems

- Mathematics
- 2011

In this paper, we propose a derivative-free method for recovering symmetric and non-symmetric potential functions of inverse Sturm-Liouville problems from the knowledge of eigenvalues. A class of…

Numerical solution of inverse Sturm--Liouville problems

- Mathematics
- 2004

A new algorithm is proposed for solving the inverse Sturm--Liouville problem of reconstructing a symmetric potential from eigenvalues. It uses Numerov's method instead of the second order method of…

## References

SHOWING 1-9 OF 9 REFERENCES

The algebraic eigenvalue problem

- Mathematics
- 1965

Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of…

Computation of derivatives of repeated eigenvalues and corresponding eigenvectors by simultaneous iteration

- Mathematics
- 1996

An earlier simultaneous iteration method for computing derivatives of eigenvalues and the corresponding eigenvectors of nonsymmetric matrices depending smoothly on some real parameters is extended to…

The Theory of Matrices

- Mathematics
- 1984

Volume 2: XI. Complex symmetric, skew-symmetric, and orthogonal matrices: 1. Some formulas for complex orthogonal and unitary matrices 2. Polar decomposition of a complex matrix 3. The normal form of…

Sensitivity analysis of all eigenvalues
of a symmetric matrix

- Mathematics
- 1995

Summary.
Given
$A(x)= [a_{ij} (x)]$ a
$n$-by-
$n$
symmetric matrix depending (smoothly) on a parameter $x$,
we study the first order sensitivity of all the eigenvalues
$\lambda_m (x)$
of
$A(x)$,…

Computation of Derivatives of Repeated Eigenvalues and the Corresponding Eigenvectors of Symmetric Matrix Pencils

- Computer ScienceSIAM J. Matrix Anal. Appl.
- 1998

New algorithms for computing the numerical values of derivatives, of arbitrary order, and of eigenvalues and eigenvectors of the hermitian matrices at a point $\rho=\rho_0$ at which the eigen values considered are multiple are analyzed.

Derivatives of eigenvalues and eigenvectors of matrix functions

- Computer Science
- 1993

Analysis is made of the existence of derivatives, the effect of normalization strategies, and the solvability and condition of the bordered matrix equations arising naturally in this context.

Design Sensitivity Analysis of Structural Systems

- Art
- 1986

This volume presents a treatment of structural design sensitivity analysis. Both the mathematical and engineering foundations of design sensitivity analysis of structural systems are examined with a…

Model Updating In Structural Dynamics: A Survey

- Computer Science
- 1993

It is the authors' hope that this work will prove to be of value, especially to those who are getting acquainted with the research base and aim to participate in the application of model updating in industry, where a pressing need exists.