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• W820331505 abstract "Methods for computing an efficient and accurate numerical solution of the real monicunilateral quadratic matrix equation,are few. They are not guaranteed to work on all problems. One of the methods performs asequence of Newton iterations until convergence occurs whilst another is a matrix analogyof the scalar polynomial algorithm. The former fails from a poor starting point and thelatter fails if no dominant solution exists. A recent approach, the Elimination method,is analysed and shown to work on problems for which other methods fail. . The methodrequires the coefficients of the characteristic polynomial of a matrix to be computed andto this end a comparative numerical analysis of a number of methods for computing thecoefficients is performed. A new minimisation approach for solving the quadratic matrixequation is proposed and shown to compare very favourably with existing methods .. A special case of the quadratic matrix equation is the matrix square root problem,where P = o. There have been a number of method proposed for it's solution, the moresuccessful ones being based upon Newton iterations or the Schur factorisation. The Eliminationmethod is used as a basis for generating three methods for solving the matrix squareroot problem. By means of a numerical analysis and results it is shown that for small orderproblems the Elimination methods compare favourably with the existing methods.The algebraic Riccati equation of stochastic and optimal control is,where the solution of interest is the symmetric non-negative definite one. The currentmethods are based on Newton iterations or the determination of the invariant subspace ofthe associated Hamiltonian matrix. A new method based on a reformulation of Newton'smethod is presented. The method reduces the work involved at each iteration by introducinga Schur factorisation and a sparse linear system solver. Numerical results suggestthat it may compare favourably with well-established methods.Central to the numerical issues are the discussions on conditioning, stability and accuracy.For a method to yield accurate results, the problem must be well-conditioned and themethod that solves the problem must be stable-consequently discussions on conditioningand stability feature heavily in this thesis.The units of measure we use to compare the speed of the methods are the operationscount and the Central Processor Unit (CPU) time. We show how the CPU time accuratelyreflects the amount of work done by an algorithm and that the operations counts of thealgorithms correspond with the respective CPU times." @default.
• W820331505 created "2016-06-24" @default.
• W820331505 creator A5089532133 @default.
• W820331505 date "1990-01-01" @default.
• W820331505 modified "2023-09-27" @default.
• W820331505 title "The numerical solution of quadratic matrix equations" @default.
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• W820331505 hasPublicationYear "1990" @default.
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