Skip to main content

Index Index

1-norm, vector, Definition
2-norm, matrix, Definition
2-norm, vector, Definition
\([ \cdot ] \), Remark
\(\epsilon_{\rm mach} \), Paragraph
\(\fl{ \cdot } \), Paragraph
\(\gamma_n \), Definition
\(\infty\)-norm, vector, Definition
\(\kappa(A)\), Definition
\(\maxi( \cdot ) \), Paragraph
\(\overline x \), Paragraph
\(\overline {~~} \), Paragraph
\(\vert \cdot \vert \), Paragraph
\(e_j \), Paragraph
\(p\)-norm, matrix, Definition
\(p\)-norm, vector, Definition
absolute value, Subsection Paragraph
Alternative Computational Model, Subsubsection Paragraph
axpy, Paragraph
backward error analysis, dot product, Section
Basic Linear Algebra Subprograms, Subsection
BLAS, Subsection
catastrophic cancellation, Subsection
Cauchy-Schwartz inequality, Paragraph Theorem
characteristic polynomial, Subsection Definition
chasing the bulge, Paragraph
Cholesky decomposition, Chapter
Cholesky factor, Paragraph
Cholesky factorization, Paragraph Chapter
Cholesky factorization theorem, Theorem
Classical Gram-Schmidt, Subsection
complex conjugate, Paragraph
condition number, Definition Definition
conjugate, Paragraph
consistent matrix norm, Definition Definition
cubic convergence, Item
defective matrix, Paragraph Definition
deflation, Subsection
determinant, Paragraph
direction of maximal magnification, Item
distance, Paragraph
dot product, backward error analysis, Section
eigenpair, Definition
eigenvalue, Definition
eigenvector, Definition
elementary elementary pivot matrix, Paragraph
equivalence style proof, Homework
error-invariant, Definition
Euclidean distance, Paragraph
floating point numbers, Subsection
forward substitution, Paragraph
Frobenius norm, Definition
Gauss transform, Subsection
Gaussian elimination, Section Subsection
Gaussian elimination with row exchanges, Subsection
Geometric multiplicity, Definition
Givens' rotation, Subsection
Gram-Schmidt orthogonalization, Section
Hermitian dot product, Definition
Hermitian inner product, Definition
Hermitian Positive Definite, Item Subsection
Hermitian positive definite, Definition
hessenberg matrix, Definition
homogeneity (of absolute value), Item
homogeneity (of matrix norm), Item
homogeneity (of vector norm), Item
Householder transformation, Paragraph Definition
Implicit Q Theorem, Theorem
induced matrix norm, Subsection Definition
infinity norm, Paragraph
Jacobi algorithm (eigenvalues and vectors), Subsection
Jordan Canonical Form, Subsection
left pseudo inverse, Definition
Legendre polynomials, Paragraph
linear convergence, Definition Item
linear least-squares, Chapter Subsubsection
linear transformation, Subsection
LU decomposition, Chapter Definition Paragraph
LU factorization, Chapter Section Definition Paragraph
LU factorization - existence, Theorem
LU factorization algorithm (bordered), Activity
LU factorization algorithm (left-looking), Paragraph
LU factorization algorithm (right-looking), Subsection
LU factorization with complete pivoting, Subsection
LU factorization with partial pivoting, Subsection
LU factorization with partial pivoting (right-looking algorithm), Subsection
LU factorization with pivoting, Section
machine epsilon, Paragraph Paragraph
magnitude, Paragraph
matrix 2-norm, Definition
matrix \(p\)-norm, Definition
matrix norm, Definition
matrix norm, 2-norm, Definition
matrix norm, \(p\)-norm, Definition
matrix norm, consistent, Definition Definition
matrix norm, Frobenius, Definition
matrix norm, induced, Subsection Definition
matrix norm, submultiplicative, Subsection Definition
matrix norm, subordinate, Definition
matrix-vector multiplication, Paragraph
Method of Multiple Relatively Robust Representations (MRRR), Subsection
Method of Normal Equations, Paragraph
method of normal equations, Section
MRRR, Subsection
norm, Chapter
norm, Frobenius, Definition
norm, infinity, Paragraph
norm, matrix, Definition
norm, vector, Definition
normal equations, Section Item
numerical stability, Chapter
orthogonal matrix, Remark
orthogonal projection, Paragraph
orthogonal vectors, Definition
orthonormal matrix, Definition
orthonormal vectors, Definition
parent functions, Item
partial pivoting, Paragraph Subsection
pivot, Paragraph
pivot element, Paragraph
positive definite, Definition
positive definiteness (of absolute value), Item
positive defnitenessx (of matrix norm), Item
positive defnitenessx (of vector norm), Item
precondition, Item
principle leading submatrix, Definition
pseudo inverse, Definition Paragraph
pseudo-inverse, Paragraph
QR algorithm, Subsection
QR decomposition, Chapter
QR Decomposition Theorem, Theorem
QR factorization, Chapter
quadratic convergence, Item
Rank-Revealing QR, Subsection
Rayleigh quotent, Paragraph
Rayleigh-quotient iteration, Subsection
reflector, Paragraph Definition
residual, Homework
right pseudo inverse, Paragraph
rowl pivoting, Paragraph
RRQR, Subsection
Schur decomposition, Subsection Theorem
Schur Decomposition Theorem, Theorem
shifted QR algorithm, Subsection
similarity transformation, Definition
Singular Value Decomposition, Chapter Paragraph
solving triangular systems, Subsection
Spectral decomposition, Subsection
spectral decomposition, Theorem
Spectral Decomposition Theorem, Theorem
spectral radius, Definition
spectrum, Definition
stability, Chapter
standard basis vector, Definition Definition
Standard Computational Model, Subsubsection Paragraph
submultiplicative matrix norm, Subsection Definition
subordinate matrix norm, Definition
superlinear convergence, Item
superquadratic convergence, Item
symmetric positive definite, Definition Paragraph
The Francis implicit QR Step, Subsection
The implicit Q theorem, Subsection
triangle inequality (for absolute value)), Item
triangle inequality (for matrix norms)), Item
triangle inequality (for vector norms)), Item
triangular system, Subsection
Tridiagonal matrix, Definition
unit ball, Subsection
unit roundoff, Paragraph
unit roundoff error, Paragraph
unitary matrix, Definition
unitary similarity transformation, Definition
upper hessenberg matrix, Definition
Vandenmonde matrix, Paragraph
vector 1-norm, Definition
vector 2-norm, Definition
vector \(\infty\)-norm, Definition
vector \(p\)-norm, Definition
vector norm, Definition
vector norm, 1-norm, Definition
vector norm, 2-norm, Definition
vector norm, \(\infty\)-norm, Definition
vector norm, \(p\)-norm, Definition
Wilkinson shift, Item