A generalized approximation theory for quadratic forms: Application to randomized spline type Sturm-Liouville problems |
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Authors: | John Gregory H R Hughes |
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Institution: | (1) Department of Mathematics, Southern Illinois University at Carbondale, 62901 Carbondale, Illinois |
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Abstract: | An approximation theory for families of quadratic forms is given. We show that if continuity conditions for a family of quadratic forms hold uniformly on an index set for the family, generalized signature approximation results hold. We then apply these results to randomized spline type Sturm-Liouville problems and obtain continuity of thenth eigenvalue for generalized Sturm-Liouville problems under weak hypotheses. |
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Keywords: | Random quadratic form Sturm-Liouville problem continuity of eigenvalues spline approximation |
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