# The Nu Class of Low-Degree-Truncated, Rational, Generalized Functions. Ia. MINOS for IMSPE Evaluation and Optimal-IMSPE-Design Search

## TL;DR

This paper introduces simplified algebraic expressions for complex integrals related to low-degree-truncated rational functions and uses MINOS optimization to identify IMSPE-optimal designs for various correlation functions, aiding design software development.

## Contribution

It provides compact algebraic formulas to replace complex integrals and applies MINOS to find optimal experimental designs for specific correlation models.

## Key findings

- Simplified algebraic expressions for integrals I6 and I8.
- Tabulated IMSPE-optimal designs for exponential, Matérn, and Gaussian correlations.
- Results serve as standards for optimal design software.

## Abstract

We provide compact algebraic expressions that replace the lengthy symbolic-algebra-generated integrals I6 and I8 in Part I of this series of papers [1]. The MRSE entries of Part I, Table 4.3 are thus updated to simpler algebraic expressions. We use MINOS [2-4] to tabulate several IMSPE-optimal designs with one factor and one or two design points, for the exponential-, two of the Mat\'ern-, and the Gaussian-correlation functions, i.e. for the class of problems considered in Part I. The tabulated results can be used as standards for optimal-design-software developers and users.

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Source: https://tomesphere.com/paper/1704.06250