Optimal properties of tensor product of B-bases
Jorge Delgado, H\'ector Orera, Juan Manuel Pe\~na
TL;DR
This paper demonstrates that the tensor product of normalized B-bases achieves optimal conditioning in the infinity norm among all normalized totally positive bases, with bounds for eigenvalues and numerical examples.
Contribution
It establishes the optimal conditioning properties of tensor product B-bases and provides bounds for eigenvalues and singular values, supported by numerical illustrations.
Findings
Optimal conditioning in infinity norm for tensor product B-bases
Bounds for minimal eigenvalue and singular value
Numerical examples confirming theoretical results
Abstract
It is proved the optimal conditioning for the infinity norm of collocation matrices of the tensor product of normalized B-bases among the tensor product of all normalized totally positive bases of the corresponding space of functions. Bounds for the minimal eigenvalue and singular value and illustrative numerical examples are also included.
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