On the condition number of local bases for piecewise cubic polynomials

Varah, J. M.

doi:10.1090/S0025-5718-1977-0428699-X

On the condition number of local bases for piecewise cubic polynomials
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by J. M. Varah PDF

Math. Comp. 31 (1977), 37-44 Request permission

Abstract:

The condition number of the Gram matrix associated with piecewise polynomial finite element bases is discussed in general, and computed explicitly for cubic splines and cubic Hermite polynomials. In the latter case, we discuss the inherent ambiguity in the basis, and find the minimum condition number.

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