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Foundation ::
Engineering Applications ::
LANZ
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LANZ
Software for Solving the Large Sparse Symmetric Generalized Eigenproblem
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Moderators:
Adopt This Application!
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SOURCE CODE AVAILABLE
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LANZ is a sophisticated algorithm based on the simple Lanczos method for
solving the generalized eigenvalue problem. LANZ uses a technique called
dynamic shifting to improve the efficiency and reliability of the basic
Lanczos algorithm. The program has been successfully used to solve problems
such as: - finding the vibration frequencies and mode shape vectors of a
structure, and
- finding the smallest load at which a structure will
buckle.
Several methods exist for solving the large symmetric generalized eigenvalue
problem. LANZ offers an alternative to the popular sub-space iteration
approach. The program includes a new algorithm for solving the tri-diagonal
matrices that arise when using the Lanczos method. Procedurally, LANZ starts
with the user's initial shift, then executes the Lanczos algorithm until:
- the desired number of eigenvalues is found;
- no storage space is left; or
- LANZ determines that a new shift is needed.
When a new shift is needed,
the program selects it based on accumulated information. At each iteration,
LANZ examines the converged and unconverged eigenvalues along with the
inertia counts to ensure that no eigenvalues have been missed.
LANZ carries the NASA case number LAR-14506. It was originally released as part of the NASA COSMIC collection.
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