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86
Applications of Sturm sequences to bifurcation
, 2003
"... analysis of delay differential equation models ..."
STURM SEQUENCES AND RANDOM EIGENVALUE DISTRIBUTIONS
"... Abstract. This paper proposes that the study of Sturm sequences is invaluable in the numerical computation and theoretical derivation of eigenvalue distributions of random matrix ensembles. We first explore the use of Sturm sequences to efficiently compute histograms of eigenvalues for symmetric tri ..."
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Cited by 4 (2 self)
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Abstract. This paper proposes that the study of Sturm sequences is invaluable in the numerical computation and theoretical derivation of eigenvalue distributions of random matrix ensembles. We first explore the use of Sturm sequences to efficiently compute histograms of eigenvalues for symmetric
MODIFIED STURM SEQUENCE PROPERTY FOR DAMPED SYSTEMS
"... ABSTRACT: Most of the eigenvalue analysis methods for the undamped or proportionally damped systems use the wellknown Sturm sequence property to check the missed eigenvalues when only a set of the lowest modes is to be used for large structures. However, in the case of the nonproportionally damped ..."
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Cited by 1 (1 self)
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ABSTRACT: Most of the eigenvalue analysis methods for the undamped or proportionally damped systems use the wellknown Sturm sequence property to check the missed eigenvalues when only a set of the lowest modes is to be used for large structures. However, in the case of the non
On A Sturm Sequence Of Polynomials For Unitary Hessenberg Matrices
 SIAM J. Matrix Anal. Appl
, 1993
"... Unitary matrices have a rich mathematical structure which is closely analogous to real symmetric matrices. For real symmetric matrices this structure can be exploited to develop very efficient numerical algorithms and for some of these algorithms unitary analogues are known. Here we present a unitar ..."
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Cited by 17 (3 self)
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unitary analogue of the bisection method for symmetric tridiagonal matrices. Recently Delsarte and Genin introduced a sequence of socalled fl n symmetric polynomials which can be used to replace the classical Szego polynomials in several signal processing problems. These polynomials satisfy a three term
1On Sturm Sequence with Floatingpoint Number Coefficients
"... Let $(P_{1}(x), P_{2}=dP_{1}/dx, P_{3}, \ldots) $ be a Sturm sequence with coefficients of floatingpoint numbers. If $P_{1} $ contains ”close ” roots the accuracy of coefficients of $P_{k} $ decreases rapidly as $k $ increases. Furthernore, the leading coefficient of some element may become abnorma ..."
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Let $(P_{1}(x), P_{2}=dP_{1}/dx, P_{3}, \ldots) $ be a Sturm sequence with coefficients of floatingpoint numbers. If $P_{1} $ contains ”close ” roots the accuracy of coefficients of $P_{k} $ decreases rapidly as $k $ increases. Furthernore, the leading coefficient of some element may become
Fast probabilistic algorithms for verification of polynomial identities
 J. ACM
, 1980
"... ABSTRACT The starthng success of the RabmStrassenSolovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a wgorous ..."
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Cited by 520 (1 self)
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and Sturm sequences are given. Probabilistlc calculatton in real anthmetlc, prewously considered by Davis, is justified ngorously, but only in a special case. Theorems of elementary geometry can be proved much more efficiently by the techmques presented than by any known arttficmlmtelhgence approach
Using Godunov’s TwoSided Sturm Sequences to Accurately Compute Singular Vectors of Bidiagonal
"... We present a hybrid scheme for computing singular vectors of bidiagonal matrices based on Godunov’s twosided Sturm sequence method [1] and Inverse Iteration [2]. This scheme is applied to the equivalent tridiagonal symmetric eigenvalue problem with corresponding matrix in the GolubKahan form. Two ..."
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We present a hybrid scheme for computing singular vectors of bidiagonal matrices based on Godunov’s twosided Sturm sequence method [1] and Inverse Iteration [2]. This scheme is applied to the equivalent tridiagonal symmetric eigenvalue problem with corresponding matrix in the GolubKahan form. Two
Sturm Sequences and the Number of Zeros of a Real Polynomial in the Unit Disk: Numerical Computation
, 1997
"... We present an efficient and precise numerical method in computational complexity and reliability to compute the number of zeros of a real polynomial in the unit disk. KeywordsPolynomials, Rootcounting method, Sturm sequence, Roundoff error analysis, Numerical computation. 1. INTRODUCTION In t ..."
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We present an efficient and precise numerical method in computational complexity and reliability to compute the number of zeros of a real polynomial in the unit disk. KeywordsPolynomials, Rootcounting method, Sturm sequence, Roundoff error analysis, Numerical computation. 1. INTRODUCTION
Regular approximations of singular SturmLiouville problems
 Results in Mathematics
"... Given any selfadjoint realization S of a singular SturmLiouville (SL) problem, it is possible to construct a sequence fS r g of regular SL problems with the properties (i) every point of the spectrum of S is the limit of a sequence of eigenvalues from the spectrum of the individual members of fS ..."
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Cited by 26 (12 self)
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Given any selfadjoint realization S of a singular SturmLiouville (SL) problem, it is possible to construct a sequence fS r g of regular SL problems with the properties (i) every point of the spectrum of S is the limit of a sequence of eigenvalues from the spectrum of the individual members of f
Results 1  10
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86