Key focus: Know the expressions to solve triangular matrix using forward and backward substituting techniques and the FLOPS required for solving it.
Consider a set of equations in a matrix form , where A is a lower triangular matrix with non-zero diagonal elements. The equation is re-written in full matrix form as
It can be solved using the following expressions
From the DSP implementation point of view, computation of requires one FLoating Point Operation per Second (FLOPS) – only one division. Computing will require 3 FLOPS – 1 multiplication, 1 division and 1 subtraction, will require 5 FLOPS – 2 multiplications, 1 division and two subtractions. Thus the computation of will require FLOPS.
Thus the overall FLOPS required for forward substitution is FLOPS
Consider a set of equations in a matrix form , where A is a upper triangular matrix with non-zero diagonal elements. The equation is re-written in full matrix form as
Solved using the following algorithm
This one also requires FLOPS.
Rate this article: (50 votes, average: 3.66 out of 5)
| [1] | An Introduction to Estimation Theory |
| [2] | Bias of an Estimator |
| [3] | Minimum Variance Unbiased Estimators (MVUE) |
| [4] | Maximum Likelihood Estimation |
| [5] | Maximum Likelihood Decoding |
| [6] | Probability and Random Process |
| [7] | Likelihood Function and Maximum Likelihood Estimation (MLE) |
| [8] | Score, Fisher Information and Estimator Sensitivity |
| [9] | Introduction to Cramer Rao Lower Bound (CRLB) |
| [10] | Cramer Rao Lower Bound for Scalar Parameter Estimation |
| [11] | Applying Cramer Rao Lower Bound (CRLB) to find a Minimum Variance Unbiased Estimator (MVUE) |
| [12] | Efficient Estimators and CRLB |
| [13] | Cramer Rao Lower Bound for Phase Estimation |
| [14] | Normalized CRLB - an alternate form of CRLB and its relation to estimator sensitivity |
| [15] | Cramer Rao Lower Bound (CRLB) for Vector Parameter Estimation |
| [16] | The Mean Square Error – Why do we use it for estimation problems |
| [17] | How to estimate unknown parameters using Ordinary Least Squares (OLS) |
| [18] | Essential Preliminary Matrix Algebra for Signal Processing |
| [19] | Why Cholesky Decomposition ? A sample case: |
| [20] | Tests for Positive Definiteness of a Matrix |
| [21] | Solving a Triangular Matrix using Forward & Backward Substitution |
| [22] | Cholesky Factorization - Matlab and Python |
| [23] | LTI system models for random signals – AR, MA and ARMA models |
| [24] | Comparing AR and ARMA model - minimization of squared error |
| [25] | Yule Walker Estimation |
| [26] | AutoCorrelation (Correlogram) and persistence – Time series analysis |
| [27] | Linear Models - Least Squares Estimator (LSE) |
| [28] | Best Linear Unbiased Estimator (BLUE) |
 Wireless Communication Systems in Matlab Second Edition(PDF) Note: There is a rating embedded within this post, please visit this post to rate it. |  Digital Modulations using Python (PDF ebook) Note: There is a rating embedded within this post, please visit this post to rate it. |  Digital Modulations using Matlab (PDF ebook) Note: There is a rating embedded within this post, please visit this post to rate it. |
| Hand-picked Best books on Communication Engineering Best books on Signal Processing | ||
This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.
Always EnabledNecessary cookies are absolutely essential for the website to function properly. These cookies ensure basic functionalities and security features of the website, anonymously.
| Cookie | Duration | Description |
|---|---|---|
| cookielawinfo-checbox-analytics | 11 months | This cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Analytics". |
| cookielawinfo-checbox-analytics | 11 months | This cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Analytics". |
| cookielawinfo-checbox-functional | 11 months | The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". |
| cookielawinfo-checbox-functional | 11 months | The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". |
| cookielawinfo-checbox-others | 11 months | This cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Other. |
| cookielawinfo-checbox-others | 11 months | This cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Other. |
| cookielawinfo-checkbox-necessary | 11 months | This cookie is set by GDPR Cookie Consent plugin. The cookies is used to store the user consent for the cookies in the category "Necessary". |
| cookielawinfo-checkbox-performance | 11 months | This cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Performance". |
| viewed_cookie_policy | 11 months | The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. It does not store any personal data. |
Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features.
PerformancePerformance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors.
Analytical cookies are used to understand how visitors interact with the website. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc.
Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet.
