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295,611
MAASS CUSP FORMS FOR LARGE EIGENVALUES
, 2004
"... We investigate the numerical computation of Maaß cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r = 40000. These eigenvalues are the largest that have so far been found in the case of the modular group. ..."
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Cited by 14 (2 self)
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We investigate the numerical computation of Maaß cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r = 40000. These eigenvalues are the largest that have so far been found in the case of the modular group
Numerical methods for large eigenvalue problems
, 2002
"... Over the past decade considerable progress has been made towards the numerical solution of largescale eigenvalue problems, particularly for nonsymmetric matrices. Krylov methods and variants of subspace iteration have been improved to the point that problems of the order of several million variable ..."
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Cited by 26 (1 self)
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Over the past decade considerable progress has been made towards the numerical solution of largescale eigenvalue problems, particularly for nonsymmetric matrices. Krylov methods and variants of subspace iteration have been improved to the point that problems of the order of several million
Preconditioned Techniques For Large Eigenvalue Problems
, 1997
"... This research focuses on finding a large number of eigenvalues and eigenvectors of a sparse symmetric or Hermitian matrix, for example, finding 1000 eigenpairs of a 100,000 \Theta 100,000 matrix. These eigenvalue problems are challenging because the matrix size is too large for traditional QR based ..."
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Cited by 4 (3 self)
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This research focuses on finding a large number of eigenvalues and eigenvectors of a sparse symmetric or Hermitian matrix, for example, finding 1000 eigenpairs of a 100,000 \Theta 100,000 matrix. These eigenvalue problems are challenging because the matrix size is too large for traditional QR based
Nonlinear component analysis as a kernel eigenvalue problem

, 1996
"... We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all ..."
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Cited by 1554 (85 self)
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We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible 5pixel products in 16x16 images. We give the derivation of the method, along with a discussion of other techniques which can be made nonlinear with the kernel approach; and present first experimental results on nonlinear feature extraction for pattern recognition.
Solution of Large Eigenvalue Problems in Electronic Structure Calculations
 BIT
, 1995
"... . Predicting the structural and electronic properties of complex systems is one of the outstanding problems in condensed matter physics. Central to most methods used in molecular dynamics is the repeated solution of large eigenvalue problems. This paper reviews the source of these eigenvalue proble ..."
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Cited by 19 (5 self)
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. Predicting the structural and electronic properties of complex systems is one of the outstanding problems in condensed matter physics. Central to most methods used in molecular dynamics is the repeated solution of large eigenvalue problems. This paper reviews the source of these eigenvalue
Solution of Large Eigenvalue Problems in Electronic Structure Calculations
 BIT
, 1996
"... Predicting the structural and electronic properties of complex systems is one of the outstanding problems in condensed matter physics. Central to most methods used in molecular dynamics is the repeated solution of large eigenvalue problems. This paper reviews the source of these eigenvalue proble ..."
Abstract
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Predicting the structural and electronic properties of complex systems is one of the outstanding problems in condensed matter physics. Central to most methods used in molecular dynamics is the repeated solution of large eigenvalue problems. This paper reviews the source of these eigenvalue
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 582 (23 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse. We discuss
Article submitted to Royal SocietySeparation of a large eigenvalue from the bulk of the spectrum
"... Separation of a large eigenvalue from the bulk of the spectrum ..."
Maaß Cusp Forms Corresponding to Large Eigenvalues
, 2002
"... of the third kind of imaginary order. SIAM J. Appl. Math., 15(5):1315 1323, 1967. A. Gil, 3. Segura, and N.M. Temme. Computation of the Modified Bessel Funktion of the Third Kind of Imaginary Orders: Uniform AiryType Asymptotic Expansion. CWI Report MASRO05, 2002. F. W. J. Olver. The asymptotic ..."
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Cited by 1 (1 self)
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expansion of Bessel functions of large order. Phil. Trans. A, 247:328 368, 1954. C. Chester, B. Friedman, and F. Ursell. An extension of the method of steepest descents. Proc. Camb. Phil. Soc., 53:599 611, 1957. 26 [24] [25] [26] [27] [28] [29] [3o] [31] [32] [33] [34] [35] [36] A. Csords, R
Results 1  10
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295,611