This paper is devoted to the condition number of the total least squares problem with linear equality constraint (TLSE). With novel  techniques, closed formulae for the 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. Explicit condition number expressions and perturbation bound for the TLS problem can be recovered from our estimates. For random TLSE problems , numerical experiments illustrate the sharpness of the estimates based on normwise condition numbers , while for sparse and badly scaled matrices, the estimates based on mixed and componentwise condition numbers are much tighter.
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.
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the condition number
condition numbers
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limit
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the
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Compact expressions and upper
Compactexpressionsandupper
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For random TLSE problems
With TLSE problems solved by the classical QR-SVD or randomized algorithms
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the sharpness of the estimates based on normwise condition numbers
that normwise condition number-based estimate is sharp to evaluate the forward error of the solution