Transcription of STURM SEQUENCES AND RANDOM EIGENVALUE …
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STURM SEQUENCES AND RANDOM EIGENVALUE DISTRIBUTIONSJAMES T. ALBRECHT, CY P. CHAN, AND ALAN paper proposes that the study of STURM SEQUENCES is invaluable in the nu-merical computation and theoretical derivation of EIGENVALUE distributions of RANDOM matrixensembles. We first explore the use of STURM SEQUENCES to efficiently compute histogramsof eigenvalues for symmetric tridiagonal matrices and apply these ideas to RANDOM matrixensembles such as the -Hermite ensemble. Using our techniques, we reduce the time tocompute a histogram of the eigenvalues of such a matrix fromO(n2+m) toO(mn) timewherenis the dimension of the matrix andmis the number of bins (with arbitrary bincenters and widths) desired in the histogram (mis usually much smaller thann).
STURM SEQUENCES AND RANDOM EIGENVALUE DISTRIBUTIONS JAMES T. ALBRECHT, CY P. CHAN, AND ALAN EDELMAN Abstract. This paper proposes that the study of Sturm sequences is invaluable in the nu-
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A Catalogue of Sturm-Liouville di erential equations, Sturm, On Sturm-Liouville Differential Equations, 6 Sturm-Liouville Eigenvalue Problems, Introduction to Sturm-Liouville Theory, Sturm-Liouville problems, Sturm-Liouvilleproblems, STURM COLLEGE OF LAW, Sturm–Liouville Problems, Sturm-Liouville Boundary Value Prob- lems, Sturm-Liouville Boundary Value Prob-lems, Sturm-Liouville Theory, Sturm Foods