# On truncated spectral regularization for an ill-posed evolution equation

## TL;DR

This paper investigates spectral truncation as a regularization technique for ill-posed parabolic final value problems, providing error estimates under noise and comparing it to Lavrentieve's method, highlighting its lack of saturation.

## Contribution

It introduces spectral truncation as a regularization method for ill-posed evolution equations and derives error estimates under general source conditions.

## Key findings

- Spectral truncation yields error estimates without saturation.
- Comparison shows spectral truncation performs favorably against Lavrentieve's method.
- Error bounds are established under noisy data conditions.

## Abstract

In this note we consider the {\it spectral truncation} as the regularization for an ill-posed non-homogeneous parabolic final value problem, and obtain error estimates under a genral source condition when the data, which consist of the non-homogeneous term as well as the final value, are noisy. The resulting error estimate is compared with the corresponding estimate under the Lavrentieve method, and showed that the truncation method has no index of saturation.