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5.0 /5
(18)

141
Bienvenido al Curso de Métodos Numéricos con Python II
Conoce nuestra trilogía de métodos numéricos
Cómo sacarle el máximo partido al curso
La Comunidad de Discord para Aprender con Amigos
El Repositorio GitHub del Curso
Toma notas de tu curso en tiempo real en Frogames Formación
Introducción al álgebra lineal numérica
Matrices
Espacios Vectoriales
Las matrices identidad, transpuesta e inversa
Tipos de matrices cuadradas
Matrices semejantes
Propiedades de las matrices
Valores y Vectores Propios
Propiedades de los Valores y Vectores Propios
Ejemplo de las relaciones entre Vaps, Veps y el teorema de Gerschgorin
Normas Vectoriales
Normas Matriciales
Norma matricial subordinada a una vectorial
Cálculo de la norma euclídea de una matriz
Cálculo de la norma 1 de una matriz
Cálculo de la norma infinito de una matriz
Ejemplos finales y propiedades
Ejercicios de álgebra lineal
Solución de la Tarea
Álgebra lineal numérica
Introducción a los sistemas de ecuaciones lineales
Simplificación de un sistema de ecuaciones lineal
El Método de eliminación de Gauss
Cómo transformar un sistema lineal en triangular superior
Ejemplo: cómo aplicar el método de Gauss a un sistema lineal
Pseudocódigo e Implementación del método de Gauss
Número de operaciones del método de Gauss
Método de Gauss con pivotaje parcial
Pseudocódigo y ejemplo de pivotaje parcial
Pivotaje parcial escalado
Pivotaje global o maximal
Método de Gauss y sus variantes
Solución de la Tarea
Factorización de matrices
Algoritmo de la descomposición LU
Algoritmo para calcular las matrices L y U
Ejemplos de aplicación del algoritmo LU
Propiedades de la descomposición LU
Matrices de permutación
Matrices de permutación y descomposición LU
Matrices diagonal dominantes
Matrices simétricas y definidas positivas
Factorización LDLt
Algoritmo LDLt
Número de operaciones
Descomposición de Choleski
Métodos directos-1
Matrices tridiagonales. Factorización de Crout
Pseudocódigo y algoritmo de Crout
Métodos de ortogonalización
Método de ortogonalización de Gram-Schmidt
Ejemplo de ortogonalización de Gram-Schmidt
Descomposición LU y LDLt
Solución de la Tarea
Descomposición QR
Pseudocódigo y algoritmo QR
Inversa de A
Cálculo de la inversa de A utilizando la descomposición LU
Cálculo de la inversa de A utilizando la descomposición QR
Determinante de una matriz A
Análisis del Error en la matriz del sistema
Análisis del Error en el vector de términos independientes
Análisis del error en general
Método QR y análisis del error
Solución de la Tarea
Métodos directos-2
Introducción a los métodos iterativos
Método de Jacobi
Pseudocódigo y ejemplo del método de Jacobi
Método de Gauss-Seidel
Pseudocódigo y ejemplo del método de Gauss-Seidel
Método Iterativo General
Lema: Convergencia de una serie de matrices
Teorema: Condición necesaria y suficiente de convergencia
Corolario: Condición suficiente de convergencia
Convergencia de los métodos de Jacobi y Gauss-Seidel
Ejemplos del estudio de la convergencia
Métodos SOR
Pseudocódigo de SOR
Teorema de Kahan
Convergencia en los métodos SOR
Métodos iterativos
Solución de la Tarea
El método del gradiente conjugado
Algoritmo del Gradiente Descendente
Direcciones de búsqueda A-ortogonales
Ortogonalidad entre los residuos y las direcciones de iteración
Construcción del Algoritmo paso a paso
Mejora de la expresión del gradiente conjugado
Pseudocódigo e implementación del algoritmo del gradiente conjugado
Gradiente Conjugado
Solución de la Tarea
Métodos Iterativos
Introducción al cálculo de valores y vectores propios
Preliminares del Método de la Potencia
Método de la Potencia
Observaciones acerca del método de la potencia
Pseudocódigo y ejemplo del método de la potencia
Aceleración de la convergencia
Matrices Simétricas
Pseudocódigo y Algoritmo para Matrices Simétricas
Método de la potencia inversa
Pseudocódigo y ejemplo del método de la potencia inversa
Técnicas de Deflación
Deflación de Wielandt
Pseudocódigo de la deflación de Wielandt
Método completo de la deflación de Wielandt con recursividad
Método de la potencia y deflación
Solución de la Tarea
Valores y vectores propios-1
Introducción a los métodos de Ortogonalización
Matrices tridiagonales simétricas
Cálculo de la sucesión de matrices
Matrices de Rotación
Cálculo de las matrices Q y S
Pseudocódigo y ejemplo del cálculo de Q y S
Pseudocódigo y ejemplo de la sucesión de matrices A^n
Matrices Hessenberg Superiores
Ejemplo del caso de matrices Hessenberg superiores
Matrices de Householder
Transformación en un matriz Hessenberg superior
Cómo calcular las matrices P de Householder
Pseudocódigo y ejemplo de Householder
Caso General del método de Householder
Métodos de ortogonalización
Solución de la Tarea
Descomposición en valores singulares
Resultados Previos del Curso de Álgebra Lineal
Algoritmo de SVD
Demostración de A = UDVt
Pseudocódigo y ejemplo de Descomposición en Valores Singulares
Descomposición en Valores Singulares
Solución de la Tarea
Valores y vectores propios-2
Enhorabuena por terminar la segunda parte del curso de métodos numéricos

instructor

5.0 /5
(18)

  • Avatar
    Angel
    (5)
    Hands-on exploration of numerical computing with Python from scratch

    This course is the second part of the numerical methods trilogy, focused on applied linear algebra. You'll learn to implement algorithms that solve systems of equations, calculate eigenvalues, decompose matrices and much more, all with Python and its scientific libraries.

  • Avatar
    Javi
    (5)
    Much clearer than I expected

    I had my doubts because matrices sounded pretty dense to me, but honestly it's explained really well. Seeing how those problems are solved so smoothly gave me a lot of confidence for my projects

  • Avatar
    María
    (5)
    A wonder for understanding linear algebra in code

    The numerical linear algebra course opened so many doors for me. Learning how to solve systems and decompose matrices computationally completely changed the way I program. Using Python was ideal. I totally recommend it to anyone looking for precision and depth.

  • Avatar
    Giovanni
    (5)
    Essential for anyone working with large volumes of data

    Learning numerical linear algebra with Python has allowed me to optimize calculation processes that were previously inefficient for me, especially highlighting the clarity in algorithm implementation and solving complex systems.

  • Avatar
    Gustavo
    (5)
    Numerical Methods with Python II – Numerical Linear Algebra: Solve Real Systems with Algorithmic Precision

    This course takes you to the heart of applied linear algebra, teaching you to solve systems of equations, compute eigenvalues, and work with matrices through efficient algorithms implemented in Python. It's the second part of a complete training in numerical methods, ideal for students of engineering, data science, and computational physics.

  • Avatar
    Jorge
    (5)
    Algebra Made Simple

    The explanations are super clear and direct, exactly what I needed to understand linear algebra better without feeling overwhelmed. Really happy with what I learned and how I was able to apply it right away.

  • Avatar
    Rosa
    (5)
    I liked this course because it's very clear in direct and iterative methods for solving linear systems

  • Avatar
    Nicolás
    (5)
    Flawless methodology

  • Avatar
    Santiago
    (5)
    Great course from the Numerical Methods collection!

  • Avatar
    Nieves
    (5)
    I was able to solve what Excel can't

    When matrices get large and manual methods fail, this course gives you the tools to solve with Python precisely

  • Avatar
    Jackeline
    (5)
    Clear, rigorous, and with practical applications in every module.

  • Avatar
    Samuel
    (5)
    The course is brutal, numerical linear algebra blew my mind.

    The practical applications in the course made me see everything differently. Now I understand concepts that seemed like a mess to me before. The course is super clear and the exercises are great for practicing.

  • Avatar
    Gabriela
    (5)
    I feel like a superhero with so many new skills

    The power of numerical linear algebra in Python is incredible. This course gave me the tools to optimize my data science projects.

  • Avatar
    Carlos
    (5)
    Linear Algebra in Python with a Practical Focus

    I recommend it to those who, like me, are looking to work with matrices and numerical systems in Python. This course is the best option—it taught me everything from the basics to advanced algorithms for solving AI and ML math problems. Great choice.

  • Avatar
    danison
    (5)
    Numerical Linear Algebra: the Key to AI and ML

    If you're looking to strengthen your applied math skills, this course is perfect. Highly recommended!

  • Avatar
    Joiser
    (5)
    great linear algebra course

    The quality of this course is a 100/10

  • Avatar
    Eulogio
    (5)
    Great course!

    I wouldn't have had so many headaches at university with this course. Really well explained and enjoyable.

  • Avatar
    BORJA
    (5)
    Excellent

    A really comprehensive course, explained really well.

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