Numerical Methods - 3.2 Linear Algebra
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 3.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{A}\mathbf{x} = \mathbf{b}}
\mathbf{A}\mathbf{x} = \mathbf{b} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | A*x = b |
A*x == b |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{A} = \mathbf{L}\mathbf{U}}
\mathbf{A} = \mathbf{L}\mathbf{U} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | A = L*U |
A == L*U |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y_{j} = f_{j}-\ell_{j}y_{j-1}}
y_{j} = f_{j}-\ell_{j}y_{j-1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | y[j] = f[j]- ell[j]*y[j - 1] |
Subscript[y, j] == Subscript[f, j]- Subscript[\[ScriptL], j]*Subscript[y, j - 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{j} = (y_{j}-u_{j}x_{j+1})/d_{j}}
x_{j} = (y_{j}-u_{j}x_{j+1})/d_{j} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle j = n-1} | x[j] = (y[j]- u[j]*x[j + 1])/(b[j]- ell[j]*c[j - 1]) |
Subscript[x, j] == (Subscript[y, j]- Subscript[u, j]*Subscript[x, j + 1])/(Subscript[b, j]- Subscript[\[ScriptL], j]*Subscript[c, j - 1]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.2#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \|\mathbf{x}\|_{p} = \left(\sum_{j=1}^{n}\abs{x_{j}}^{p}\right)^{1/p}}
\|\mathbf{x}\|_{p} = \left(\sum_{j=1}^{n}\abs{x_{j}}^{p}\right)^{1/p} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error
|
Subscript[Norm[x], p] == ((Sum[(Abs[Subscript[x, j]])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)
|
Failure | Failure | Error | Failed [300 / 300]
Result: Plus[-1.0, Subscript[1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]
Test Values: {Rule[n, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Plus[Complex[-1.7142646344505674, 0.6191072997114272], Subscript[1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]
Test Values: {Rule[n, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5], Rule[Subscript[x, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |
| 3.2.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\|\mathbf{x}^{*}-\mathbf{x}\|_{p}}{\|\mathbf{x}\|_{p}} \leq \kappa(\mathbf{A})\frac{\|\mathbf{r}\|_{p}}{\|\mathbf{b}\|_{p}}}
\frac{\|\mathbf{x}^{*}-\mathbf{x}\|_{p}}{\|\mathbf{x}\|_{p}} \leq \kappa(\mathbf{A})\frac{\|\mathbf{r}\|_{p}}{\|\mathbf{b}\|_{p}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Error |
Divide[Subscript[Norm[(x)^(*)- x], p],Subscript[Norm[x], p]] <= (Subscript[Norm[A], p]*Subscript[Norm[(A)^(- 1)], p])*Divide[Subscript[Norm[r], p],Subscript[Norm[b], p]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 3.2.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathbf{A}\mathbf{x} = \lambda\mathbf{x}}
\mathbf{A}\mathbf{x} = \lambda\mathbf{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | A*x = lambda*x |
A*x == \[Lambda]*x |
Skipped - no semantic math | Skipped - no semantic math | - | - |