By Richard B. Lehoucq, Danny C. Sorensen, C. Yang
A consultant to realizing and utilizing the software program package deal ARPACK to unravel huge algebraic eigenvalue difficulties. The software program defined is predicated at the implicitly restarted Arnoldi procedure. The ebook explains the purchase, deploy, services, and distinct use of the software program.
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Extra resources for ARPACK Users' Guide: Solution of Large-scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods
This discussion is intended to give a broad overview of the theory and to develop a high-level description of the algorithms. Specific implementation details concerned with efficiency and numerical stability are treated in Chapter 5. The remainder of this chapter will develop enough background to understand the origins, motivation, and expected behavior of this algorithm. The discussion begins with a very brief review of the structure of the algebraic eigenvalue problem and some basic numerical methods that either influence or play a direct role in the IRAM.
For example, if the matrix is indefinite then setting which = 'SM J will require interior eigenvalues to be computed and the Lanczos process may require many steps before these are resolved. For a given ncv, the computational work required is proportional to n • ncv2 FLOPS. Setting nev and ncv for optimal performance is very much problem dependent. If possible, it is best to avoid setting nev in a way that will split clusters of eigenvalues. For example, if the five smallest eigenvalues are positive and on the order of 10~4 and the sixth smallest eigenvalue is on the order of 10"1 then it is probably better to ask for nev = 5 than for nev = 3, even if the three smallest are the only ones of interest.
The relation between the eigenvalues of OP and the eigenvalues of the original problem must also be understood in order to make the appropriate specification of which in order to recover eigenvalues of interest for the original problem. The user must specify the number of eigenvalues to compute, which eigenvalues are of interest, the number of basis vectors to use, and whether or not the problem is standard or generalized. 2 of Chapter 2. Setting nev and ncv for optimal performance is very much problem dependent.
ARPACK Users' Guide: Solution of Large-scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods by Richard B. Lehoucq, Danny C. Sorensen, C. Yang