# Iterative Methods for Computing Vibrational Spectra

## Abstract

**:**

**F**) matrix. The second uses Smolyak quadrature and a pruned basis. The third uses a tensor rank reduction scheme.

## 1. Introduction

## 2. Direct Product Basis Sets

## 3. Using a Direct Product Basis Set to Solve the Schroedinger Equation

## 4. Using a DVR to Make a Contracted Basis

#### Evaluating Matrix-Vector Products without Storing a Vector as Large as the Direct Product DVR

**F**matrix [6] defined by,

## 5. Using Pruning to Reduce Both Basis and Grid Size

## 6. Using Rank Reduction to Avoid Storing Full Dimensional Vectors

## 7. Conclusions

## Acknowledgments

## Conflicts of Interest

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Carrington, T., Jr. Iterative Methods for Computing Vibrational Spectra. *Mathematics* **2018**, *6*, 13.
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