
Leastsquares spectral methods for ODE eigenvalue problems
We develop spectral methods for ODEs and operator eigenvalue problems th...
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Full operator preconditioning and the accuracy of solving linear systems
Unless special conditions apply, the attempt to solve illconditioned sy...
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Fast randomized numerical rank estimation
Matrices with lowrank structure are ubiquitous in scientific computing....
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Stable and Efficient Computation of Generalized Polar Decompositions
We present methods for computing the generalized polar decomposition of ...
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Zolotarev's fifth and sixth problems
In an influential 1877 paper, Zolotarev asked and answered four question...
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Twice is enough for dangerous eigenvalues
We analyze the stability of a class of eigensolvers that target interior...
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Reciprocallog approximation and planar PDE solvers
This article is about both approximation theory and the numerical soluti...
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Fast and stable randomized lowrank matrix approximation
Randomized SVD has become an extremely successful approach for efficient...
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Solving twoparameter eigenvalue problems using an alternating method
We present a new approach to compute selected eigenvalues and eigenvecto...
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Exponential node clustering at singularities for rational approximation, quadrature, and PDEs
Rational approximations of functions with singularities can converge at ...
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Rational neural networks
We consider neural networks with rational activation functions. The choi...
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Vandermonde with Arnoldi
Vandermonde matrices are exponentially illconditioned, rendering the fa...
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Weighted Monte Carlo with least squares and randomized extended Kaczmarz for option pricing
We propose a methodology for computing single and multiasset European o...
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An algorithm for real and complex rational minimax approximation
Rational minimax approximation of real functions on real intervals is an...
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Accuracy of approximate projection to the semidefinite cone
When a projection of a symmetric or Hermitian matrix to the positive sem...
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Approximating the pth Root by Composite Rational Functions
A landmark result from rational approximation theory states that x^1/p o...
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On orthogonal tensors and best rankone approximation ratio
As is well known, the smallest possible ratio between the spectral norm ...
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Yuji Nakatsukasa
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