Textbooks Numerical Linear Algebra
Book Cover for Numerical Linear Algebra

Numerical Linear Algebra

Lloyd N. Trefethen, David Bau III 1st Edition ISBN #9780898713619 162 Questions
7,772 Students Work From this Textbook

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Chapters

1

Matrix-Vector Multiplication

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4 questions
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2

Orthogonal Vectors and Matrices

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7 questions
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3

Norms

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6 questions
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4

The singular Value Decomposition

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5

More on the SVD

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6

Projectors

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7

QR Factorization

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9 questions
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8

Gram-Schmidt Orthogonalization

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9

MATLAB

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10

Householder Triangularization

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11

Least Squares Problems

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12

Conditioning and Condition Numbers

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13

Floating Point Arithmetic

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14

Stability

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15

More on Stability

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16

Stability of Householder Triangularization

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17

Stability of Back Substitution

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18

Conditioning of Least Squares Problems

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19

Stability of Least Squares Algorithms

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20

Gaussian Elimination

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21

Pivoting

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22

Stability of Gaussian Elimination

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23

Cholesky Factorization

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24

Eigenvalue Problems

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25

Overvicw of Eigenvalue Algorithms

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26

Reduction to Hessenberg or Tridiagonal Form

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27

Rayleigh Quotient, Inverse Iteration

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28

QR Algorithm without Shifts

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29

QR Algorithm with Shifts

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30

Other Eigenvalue Algorithms

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31

Computing the SVD

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32

Overview of Iterative Methods

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33

The Arnoldi Iteration

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34

How Arnoldi Locates Eigenvalues

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35

GMRES

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36

The Lanczos Iteration

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37

From Lanczos to Gauss Quadrature

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38

Conjugate Gradients

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39

Biorthogonalization Methods

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40

Preconditioning

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