Linear inference problems with deterministic constraints

TL;DR

This paper presents advanced methods for solving linear inference problems with deterministic constraints, improving upon classical approaches and demonstrating efficiency through numerical examples in spherical harmonic coefficient estimation.

Contribution

It introduces novel advances addressing conceptual and practical issues in linear inference with deterministic constraints, extending classical methods.

Findings

Methods can efficiently estimate spherical harmonic coefficients from point data.

Numerical examples demonstrate practical applicability to realistic problems.

Approaches improve upon previous techniques in accuracy and computational efficiency.

Abstract

Methods are described for the solution of linear inference problems subject to deterministic constraints. The approach builds on work by Backus (1970a,b,c) and Parker (1977), but a range useful advances are suggested to address both conceptual and practical issues. The theory is motivated by, and illustrated with, the estimation of a finite number of a function's spherical harmonic coefficients from a finite set of its point values. Numerical examples are included to demonstrate that the methods can be efficiently applied to realistic problems.