Tag: Matrix Theory and Algorithms
Generic cuspidal points can be localized from eigenvalue loops
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in MathematicsWhat the study found The study finds that generic cuspidal points, meaning parameter values where eigenvalues coalesce in smooth complex-valued matrix functions of two parameters, can be analyzed through loops in parameter space. It also states that phase accumulation for eigenvectors can occur around such loops, and that eigenvalue periodicity and phase accumulation may help…
Schur multiplier norm and its dual are expressed by minimization formulas
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in MathematicsWhat the study found The study shows that for a complex self-adjoint matrix, the Schur multiplier norm can be determined by a minimization formula involving a diagonal bound. It also gives a corresponding formula for the dual norm of the Schur multiplier norm. Why the authors say this matters The authors say they study the…
Modified conjugate gradient method showed better numerical performance
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in MathematicsWhat the study found The paper reports that a modified conjugate gradient coefficient method was developed for solving unconstrained optimization problems. The authors state that the method uses a strong Wolfe line search and that numerical results showed improved performance compared with other conjugate gradient methods. Why the authors say this matters The study suggests…
