Numerical solution of separable nonlinear equations with a singular matrix at the solution

DOI10.1007/S11075-019-00861-0zbMath1456.65033OpenAlexW2997611296WikidataQ126394971 ScholiaQ126394971MaRDI QIDQ827071

Tjalling J. Ypma, Yun-Qiu Shen

Publication date: 6 January 2021

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-019-00861-0

zbMATH Keywords

bordered matrixsingular matrixGauss-Newton methodnonlinear least squaresseparable nonlinear equations

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Cites Work

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• Solving rank-deficient separable nonlinear equations
• Solving nonlinear systems of equations with only one nonlinear variable
• Regularization methods for uniformly rank-deficient nonlinear least-squares problems
• The variable projection algorithm in time-resolved spectroscopy, microscopy and mass spectrometry applications
• An efficient algorithm for the separable nonlinear least squares problem
• Solving separable nonlinear least squares problems using the QR factorization
• Solving separable nonlinear equations using LU factorization
• Solving \(N+m\) nonlinear equations with only m nonlinear variables
• Rank deficiencies and bifurcation into affine subspaces for separable parameterized equations
• Separable nonlinear least squares: the variable projection method and its applications
• Truncated Gauss–Newton algorithms for Ill-conditioned nonlinear least squares problems
• The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate

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