TThis paper is devoted to condition numbers of the total least squares problem with linear equality constraint (TLSE). With novel limit techniques, closed formulae for normwise, mixed and componentwise condition numbers of the TLSE problem are derived. Compactexpressionsandupper bounds for these condition numbers are also given to avoid the costly Kronecker product-based operations. Explicit condition number expressions and perturbation bound for the TLS problem can be recovered from our estimates. With TLSE problems solved by the classical QR-SVD or randomized algorithms , numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.
This paper is devoted to condition numbers of the total least squares problem with linear equality constraint (TLSE). With novel limit techniques, closed formulae for normwise, mixed and componentwise condition numbers of the TLSE problem are derived. Compact expressions and upper bounds for these condition numbers are also given to avoid the costly Kronecker product-based operations. The results unify the ones for the TLS problem . For TLSE problems with equilibratory input data , numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, mixed and componentwise condition numbers-based estimations are much tighter.
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TThis
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Compactexpressionsandupper
Compact expressions and upper
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Explicit condition number expressions and perturbation bound
The results unify the ones
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can be recovered from our estimates. With TLSE problems solved by the classical QR-SVD or randomized algorithms
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the estimates based on
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numbers
numbers-based estimations