Solving generalized inverse eigenvalue problems via L-BFGS-B method
Zeynab Dalvand, Masoud Hajarian
Abstract
The parameterized generalized inverse eigenvalue problems containing multiplicative and additive inverse eigenvalue problems appear in vibrating systems design, structural design, and inverse Sturm–Liouville problems. In this article, by using the Cholesky factorization and the Jacobi method, we propose two efficient algorithms based on Newton's method and the L-BFGS-B method for solving these problems. To demonstrate the effectiveness of the algorithms, we present three numerical examples.
Topics & Concepts
Broyden–Fletcher–Goldfarb–Shanno algorithmCholesky decompositionEigenvalues and eigenvectorsParameterized complexityRayleigh quotient iterationInverseMathematicsApplied mathematicsInverse iterationInverse problemEigendecomposition of a matrixDivide-and-conquer eigenvalue algorithmMultiplicative functionMultiplicative inverseMathematical optimizationComputer sciencePreconditionerMathematical analysisAlgorithmIterative methodGeometryPhysicsQuantum mechanicsAsynchronous communicationComputer networkMatrix Theory and AlgorithmsTopology Optimization in EngineeringComposite Structure Analysis and Optimization